Allardyce made nine changes from the team which lost to Fulham in the Premier League last weekend for the cup clash at the City Ground with youngsters Seb Lletget, Danny Whitehead and Callum Driver all making their first appearances.
With a League Cup semi-final first leg at Manchester City to come on Wednesday, Allardyce, already under pressure with his side second from bottom in the Premier League, said he had no choice but to ring the changes.
"What choice (in terms of team selection) did I have? I don't think I had one," he told reporters.
"I make the decisions for the benefit of everyone at the football club. We have a huge amount of problems in terms of available players.
"We have a League Cup semi-final against Manchester City and the main priority is to get to Wembley. My changes had to be severe today, I didn't want it to be."
West Ham were undone by goals from Djamel Abdoun and Andy Reid either side of a second-half hat-trick from Jamie Paterson to leave Allardyce facing fresh questions about his future.
His side have picked up just 15 points from their opening 20 league games and are three points short of the Premier League's safety zone.
Having splashed a club-record transfer fee on recruiting Andy Carroll on a permanent deal in the close season, the club have yet to see any return on their investment with the striker out injured and yet to make an appearance this season.
West Ham keeper Adrian tried to keep up the spirits of the club's dejected fans in the wake of Sunday's game.
"Sorry to all West Ham fans for this regrettable match. Now, change to a positive mentality and think the next game vs. Man City!," he said on Twitter.
(Reporting by Toby Davis; editing by Martyn Herman)
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