Rampant City thrashed the Hammers 6-0 in the first leg of their Capital One Cup semi-final at the Etihad Stadium, turning up the heat even more on manager Allardyce.
The London club were humbled 5-0 by Sky Bet Championship side Nottingham Forest in the FA Cup last weekend and, as they sit 19th in the Barclays Premier League, supporters' patience is wearing thin.
Allardyce was publicly backed by the club's owners earlier in the week but their fans had become abusive by the end of another tough night.
Allardyce said: "It is life isn't it when you are not doing well - you get stick as a manager and I am getting stick at the moment.
"That is the way goes, that is the way this job is you take it on the chin and get on with it.
"We are not the first team to get beaten here by many, many goals and we won't be the last having seen Manchester City through this season.
"But you cannot keep losing football matches, that is for sure, as a manager.
"You cannot think it will be allowed to continue. I don't want it to continue, that is for sure.
"We have to get those (injured) players back as quick as we can and we have got to not lose confidence in our own ability and get out of this hole we are in at the moment."
West Ham have been ravaged by injuries, robbing Allardyce of the likes of Winston Reid, James Collins and Andy Carroll while Kevin Nolan was suspended.
Because of that Allardyce felt his below-strength team were ill-equipped to deal with a City team again at their devastating best.
Alvaro Negredo fired a hat-trick while Edin Dzeko also struck twice and Yaya Toure got on the scoresheet.
Allardyce said: "We fought very hard to get to the semi-final, we played some great games and won some fantastic football matches, but unfortunately this semi-final fell at the wrong moment in time and they punished us.
"You can't get near a team when they play like that. People will think they haven't tried.
"They tried but their best wasn't good enough with the quality and talent of the players they have got."
Allardyce had prioritised the match to an extent by fielding a deliberately weakened side at Forest.
Now that has doubly backfired, Saturday's league trip to Cardiff takes on huge significance.
Allardyce said: "We have to get our heads up and our shoulders back and our chest out, and start believing that we are going to do better - starting with Cardiff."
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