The London club, who lost 5-0 to second tier Nottingham Forest in the FA Cup on Sunday, were taken apart by Manchester City F.C.'s free-scoring side in a mis-match that effectively ended their hopes of reaching the Wembley final.
Allardyce, whose squad has been severely depleted by injuries, said the result was down to the simple matter of money.
"They are a side who have outstanding players because they spend outstanding money," he said on Sky Sports.
"What do you expect when you have free transfers against players who cost millions and millions
"Let's face the fact, Manchester City F.C. have a miles better squad and are on miles better money. For us it is about not letting the players get too low."
Allardyce's position at West Ham has come under scrutiny with the London club currently 19th in the Premier League and facing a scrap to avoid relegation to the second tier.
They gambled on signing striker Andy Carroll from Liverpool on a big-money permanent deal in the close season, but have yet to see any return on their investment.
Carroll has only just returned to training having missed the start of the season through injury.
West Ham are in a perilous position having won one of their last 13 league matches, but the club's owners publicly backed their manager this week in an open letter to fans.
"They (the owners) really mean it because we keep talking and communicating," Allardyce said.
"We are actively communicating between each other on the injured front and trying to bring players into the club."