The Dons, base of the third level of English football, flooded into a 3-0 lead against the Premier League side affability of Kwesi Appiah's redirected strike and Scott Wagstaff's twofold either side of half-time.
Pellegrini made a triple substitution at the break trying to get once again into the diversion and saw two of his changes - Lucas Perez and Felipe Anderson - score to make it 3-2.
Be that as it may, AFC Wimbledon, who were beaten 3-0 at home by Fleetwood in their keep going class amusement on Tuesday, kept on driving men forward and put the seal on a well known triumph kindness of Toby Sibbick's late short proximity header, starting scenes of celebration among the home group and leaving Pellegrini enraged.
"Is it safe to say that i was irate at half-time? Indeed obviously - I was embarrassed about them," said Pellegrini.
"It's anything but difficult to clarify what occurred - it was one group who needed to win and another group who played with no craving or any aspiration to win or proceed in this glass.
"Possibly we thought we were going to win since we are a Premier League group and they are in League One, however Wimbledon played with the craving to contend in this glass. In the initial 45 minutes, we didn't battle.
"It's extremely baffling in light of the fact that you can be disposed of, however not in the manner in which we were. It's a calamity."
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Arnautovic signs new West Ham bargain
The Dons' certain methodology compensated with well known triumph
AFC Wimbledon's Scott Wagstaff
Scott Wagstaff scored the first of his two objectives without further ado before half-time to put AFC Wimbledon 2-0 ahead
AFC Wimbledon were playing in the fourth round of the FA Cup out of the blue since they transformed in 2002, yet this completely merited triumph has made another bit of history that reviewed the Crazy Gang soul of Wimbledon's renowned 1988 FA Cup last win over Liverpool.
The Dons are five afloat at the foot of League One yet gave a false representation of their modest group position by commanding West Ham for a significant part of the diversion, especially amid the principal half.
Terell Thomas had an early chance, however bursted over when all around set inside the container before Mitchell Pinnock's header was spared by goalkeeper Adrian.
Yet, similarly as West Ham thought they had endured the AFC Wimbledon storm, the home side led the pack.
Anthony Wordsworth's perfect pass discovered Appiah and his exertion from simply outside the region avoided off Angelo Ogbonna and past a wrong-footed Adrian
AFC Wimbledon kept on squeezing and their inspirational frame of mind was remunerated again in a matter of seconds before the break.
Wagstaff stole the ball off Obiang in midfield before driving forward and completing low into the corner.
You could comprehend on the off chance that the Dons had, hoped to protect and keep what they had, yet rather they kept on pushing forward and proceeded seconds after the restart kindness of Wagstaff's slick flick from Appiah's cross.
Notwithstanding when West Ham decreased the back payments to 3-2, AFC Wimbledon kept on driving men forward and were compensated when 19-year-old substitute Sibbick gestured home Wordsworth's prodding cross to seal the success.
Dylan Connolly - making his first AFC Wimbledon begin since joining from Dundalk toward the beginning of this current month - symbolized their positive methodology. The 23-year-old Irishman was a consistent danger down the correct flank and was deservedly given an overwhelming applause when he was substituted late on.
Administrator Wally Downes, a previous Wimbledon player during the 1980s, just came back to the club in December.
Pulling the club far from the foot of the table is probably going to be his need, yet he presently gets the opportunity to make more FA Cup history 31 years after that well known evening at Wembley.
Messy West Ham droop to crush
Talking before the amusement, Pellegrini had asked his West Ham players to demonstrate a "triumphant mindset" to guarantee they would not be the casualty of a container stun and named a solid beginning line-up.
Marko Arnautovic, who has recently marked another agreement, was a striking non-attendant, yet there were begins for any semblance of Andy Carroll, Javier Hernandez and Mark Noble.
In any case, the Hammers essentially did not get moving in the main half, neglecting to gather a shot on target.
Their solitary exertion of note was a diverted Hernandez shot that cut the outside of the post.
At the opposite end, Arthur Masuaku attempted to adapt to AFC Wimbledon's assaults down the left while Obiang's blunder just before half-time permitted Wagstaff to score the house side's urgent second.
Pellegrini reacted by making the triple substitution at the break, expediting Perez, Anderson and Ryan Fredericks, just to see his side yield inside a moment of the restart.
The Chilean looked exasperated on the touchline with his side apparently out of answers, however they indicated soul to drag themselves once again into the diversion on account of two of Pellegrini's substitutes.
First Perez was aware of drive the ball into the corner after Michail Antonio's shot had been spared by Aaron Ramsdale.
Anderson at that point demonstrated a bit of class to twist home a great free-kick from simply outside the territory for his ninth objective of the season.
However, the Hammers kept on looking powerless at the back and they can have couple of protests with the outcome, as they were disposed of by a League One side in the fourth round for a second progressive year.
'I could have changed every one of the players' - what they said
AFC Wimbledon chief Wally Downes addressing BT Sport: "I don't know whether it was an arrangement, winning was the arrangement, not the 4-2.
"What was imperative was that they got over Tuesday's execution [3-0 home annihilation by Fleetwood]. It was an extraordinary diversion to overwhelm the webs and they did.
"Football is arbitrary. There is a heap of investigation we do, me notwithstanding, however on some random day, any group can beat some other group and we have done it today around evening time.
"They are a passing group yet with Andy Carroll in the side they need to go direct and they may have gotten between the two. We realized it was vital to stop Mark Noble taking care of business the ball."
West Ham administrator Manuel Pellegrini addressing the club's legitimate site: "I changed three players since I could just roll out three improvements. I could have changed every one of the players. Tragically for us, they scored their third objective in the first or second moment of the second half, which made it exceptionally troublesome.
"We talked before the amusement that this diversion happens a ton of time where the group in the lower division beats the group which is better since they play each ball as though it is their last chunk of the amusement. We didn't have that disposition and when we would, we be able to didn't attempt.
"The pace of the diversion, the manner in which we battled for each ball and the manner in which we made developments to get the ball were baffling. I changed three players since I could just roll out three improvements. I could have changed every one of the players. Lamentably for us, they scored their third objective in the first or second moment of the second half, which made it exceptionally troublesome."
AFC Wimbledon make history - the details
AFC Wimbledon scored more than one objective in a solitary match in the FA Cup appropriate against a side from a higher division for the absolute first time in what was their tenth such challenge since they transformed in 2002.
It is additionally simply the second time AFC Wimbledon have advanced from a FA Cup appropriate tie against a side from a higher division, and the first since they beat Scunthorpe United in a first-round replay in 2011-12.
AFC Wimbledon's Scott Wagstaff scored his first-since forever prop in expert football - he had scored only two objectives in his last 44 appearances in all rivalries previously the success over West Ham.
West Ham have been killed from the FA Cup by a League One side for a second continuous crusade after Wigan beat them in 2018; it is the first occasion when they have been thumped out of the challenge by sides from a lower division in consecutive competitions since 1998-99 (Swansea City) and 1999-00 (Tranmere Rovers).
West Ham have yielded four objectives in a solitary FA Cup amusement against a side from the third level or underneath out of the blue since January 1936 when they lost 4-0 to Luton Town in a third-round replay.
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