The result, coming just four days after a 5-0 humbling by Forest in the FA Cup, turned up the heat on Allardyce ahead of Saturday's critical visit to Cardiff in the Barclays Premier League.
The Hammers are 19th in the table and have not won in the league since November.
The visiting supporters may not have expected much at City, and they initially reacted to their predicament with humour, but as the goals poured in the atmosphere turned abusive.
Allardyce vowed to take that on the chin and pledged to fight on, but he has a tough task on his hands to rally his squad.
Allardyce said: "There are times when it is good and there are times when it is not so good.
"You have to accept that when it is not so good you have to draw on your strengths and experience to guide the players through the difficult time you are facing.
"Picking them up and getting them ready for the next game is my job.
"At the end of the day, we cannot keep walking around with our heads down and doom and gloom."
Allardyce's cause has not been helped this season by a catalogue of injuries to key players.
Star striker Andy Carroll has not played since making his move from Liverpool permanent last summer, while the likes of James Collins, James Tomkins, Winston Reid and Ricardo Vaz Te are also out. In addition, captain Kevin Nolan is presently suspended.
West Ham will still need to go through the motions of their second leg against City, but Allardyce knows the tie is effectively over and he needs to focus on the relegation battle.
He said: "My most important two games now are Cardiff City, in a couple of days, and Newcastle, before we get to the second leg.
"That is the biggest and major concern for me, getting up and getting the lads ready for that."
The Hammers were soon on the back foot against City and conceded when Alvaro Negredo scored the first goal of his hat-trick after 12 minutes.
Edin Dzeko struck twice and Yaya Toure was also on target for rampant City.
The hosts might have had several more in an embarrassingly one-sided contest but goalkeeper Adrian did come to the Hammers' rescue a number of times.
The only crumb of consolation for Allardyce was that his team are merely the latest in a growing list to have been vanquished at Eastlands.
Arsenal conceded six there last month, Tottenham lost 6-0, Norwich 7-0 and champions Manchester United were routed 4-1.
Allardyce said: "When you have got none of your real defenders and have a free transfer in and a left-back playing at centre-half against Negredo and Dzeko, it shows you the gulf.
"It is not very pleasant and it is unfortunate for us that we are playing Manchester City low on confidence and with too many injuries.
"But if we were the only side who got beat here 6-0, it would be more of a worry."
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