Allardyce admitted it was "more than a tad disappointing" not to have been able to close out what would have been a memorable victory.
He said: "You have never beaten Manchester United until the final whistle blows and I have learned that in the past.
"When Matt Jarvis broke down the left-hand side late on and put in a great ball for Mark Noble to head down to Matt Taylor I was going, 'Please put it in', because Manchester United weren't going to come back from that.
"But if we didn't put it in it would be nail-biting until the final whistle because somewhere along the line they might just carve out a chance with the quality that they have got.
"It was just a brilliant goal they scored.... the ball from Ryan Giggs, who smashed a half-volley over James Tomkins' head from about 60 yards, and Van Persie's first touch and finish were just unbelievable."