The Hammers have endured a terrible recent run, being knocked out of the FA Cup 5-0 at Nottingham Forest before going down to a 6-0 Capital One Cup semi-final first-leg defeat at Manchester City in the past week.
Allardyce's men are only a point above bottom club Sunderland in the table before travelling to the Welsh capital - and the United boss wrote on the club's official website in a weekly address to fans: "Many teams have gone to Manchester City and, like us, have suffered a painful time.
"It's hard to take and difficult to accept but the facts are that Manchester City are the best team in the league at home and have been the best team in the league since the start of the season.
"We all knew they were very, very good and we've seen it live because our players tried as hard as they could, but couldn't get near these Manchester City players. Their quality is top-drawer and they are great finishers, never mind top footballers."
The former Bolton, Blackburn and Newcastle boss reserved special praise for Adrian, despite the Spanish goalkeeper shipping 11 goals in the past two games.
Allardyce added: "Despite the scoreline, Adrian was brilliant and he's growing stronger. He's gaining great experience, even if he is bitterly disappointed about Sunday and Wednesday. He played well on Sunday but he played even better on Wednesday.
"What we have to do now is get our defenders back in the team defending like we know we can, as a team, better. We have got to improve our clean-sheet ratio as quickly as possible and once we start doing that, we'll start winning more points and hopefully more games."
Allardyce now wants his players to use their recent humiliations as a springboard for better performances and has called on them to prove their critics wrong.
"They can't feel sorry for themselves," he added on West Ham TV. "We are professionals and we've got to take the criticism thrown at us because that's what happens in the game at this level.
"We've got to be man enough to take it on the chin and be determined enough to show people what they think at this particular moment in time is wrong.
"You either come out fighting or you sink and die - I come out fighting as a manager and my staff and players are the same.
"We've got to get out there, face the music and use it to anger us, if you like, make us mad, prove them wrong and win football matches."