The Upton Park club came within seconds of eliminating their Premier League rivals in London on Saturday evening after taking a 2-1 lead into injury time.
And after on Friday re-joining West Ham from Liverpool, boyhood Hammer Cole had been one of the main architects, setting up two James Collins headers to cancel out Tom Cleverley's opener.
Robin van Persie's wonderful injury-time equaliser ultimately forced a replay but Allardyce was still full of praise for Cole and his team, as the manager told West Ham's official website: "He is a top international player for England and he played for the top team in the country at Chelsea.
"He had a move that went wrong to Liverpool so you could relate it to Steven Pienaar, who went from Everton to Tottenham and it didn't work, then he has gone back and it's gone well.
"Joe is still in his early thirties and, as long as he stays fit for me - we'll work hard at doing that - then he will be a great asset."
Manchester United manager Sir Alex Ferguson admitted his side were not at their best and Allardyce had thought West Ham would be good value to win after a quiet game for goalkeeper Jussi Jaaskelainen.
"Everybody was outstanding. The only one who wasn't was Jussi, because he didn't have anything to do," said Allardyce.
"What does that say about the performance? If he had saved Van Persie's shot, he'd have been the hero, because I think we'd have won the game."