United raced into a three-goal lead before Carlton Cole grabbed a late consolation for the visitors.
Speaking to Sky Sports after the game, Allardyce could not hide his disappointment at the result.
Allardyce said: "I think we made the victory too easy for them. I didn't think we made them work hard enough for it.
"We made silly mistakes and when Manchester United get a sniff like that they are not going to turn it down. We did get better in the second half and played a little more like we know we can but it was too late for us to try and get any points.
"From my point of view there were a few players who didn't play against Tottenham in the week who I expected more from. Those that did play were tired at the end but some should have contributed more."
Allardyce handed a Premier League debut to goalkeeper Adrian and thought he performed well.
Allardyce added: "I haven't seen the goals but from our point of view we'll look at his overall performance tomorrow, as we do all the players, but it looked like he had a good game."
West Ham entertain Arsenal on Boxing Day before rounding off 2013 with a game against West Brom at Upton Park next Saturday.