Robin van Persie broke the deadlock at Old Trafford after just 33 seconds, as his guided effort deflected off of James Collins and into the net.
The Hammers were unable to respond, but Allardyce believes only luck separated the two sides:
“We come to Old Trafford and in 30 seconds they score,” he told SkySports.
“It was a fluke goal, to say the least.
“It was a test of character for my players. We are all disappointed that we lost the match, but we kept our shape and our tactics.
“We couldn’t help the fluke goal fortunately for Man United. You never know what could have happened if that had not gone in.
“It is disappointing that after all that we did not get anything from the game.
“I was pleased with the energy we had, especially in the latter end of the game. The energy that we showed today was outstanding.”
Allardyce went on to suggest that the goal scorer may well be a decisive factor in this season’s title race:
“Robin van Persie is a quality player and we have largely kept him quiet.
“But he will score 20 goals for Manchester United, maybe 30. In the end that is normally the difference.”