The Dutchman scored his 12th goal of the season just 33 seconds into Manchester United's encounter with the Hammers at Old Trafford.
"Manchester United have lots of players who will have good spells and can come up trumps when they need them to," said Allardyce. " 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."
Allardyce could take plenty of positives out of his first visit to Old Trafford as a visiting manager since he presided over a 7-1 defeat for Blackburn two years ago.
When Van Persie struck so early, the Hammers might have feared something similar. In the end, though, they were the ones who finished stronger, only for Carlton Cole to waste their best chance when it was saved by Anders Lindegaard.
"It is a big problem to concede after 30 seconds," said Allardyce. "But our response was very good. We didn't create much but we went looking for the equaliser and the best chance fell to Carlton Cole when he didn't quite catch it.
"Whether Manchester United played to their potential or not doesn't matter does it? They still won. They have a nasty habit of doing that."
"We got a great start," said Ferguson. "You hope to go on from a start like that and some of our football was very good but we never quite finished them off.
"We have played with the diamond quite a few times this season and done very well so I don't think that is an excuse. But we have got the three points and are still ahead in the league."