Rooney netted a double to help the reigning Premier League champions to victory at Upton Park on Saturday, with his first goal grabbing all the headlines.
He hit an audacious half-volley from just inside the opposition half that looped over stranded West Ham goalkeeper Adrian to open the scoring in the eighth minute.
The England international's strike will surely be considered a goal-of-the-season contender, but while Allardyce could not deny the technical quality of Rooney's strike, he felt that referee Lee Mason should have awarded a foul in the build-up after James Tomkins was impeded.
"It was such a wonderful goal from Wayne Rooney early on," said the West Ham boss. "No one expected him to do that, not even David Moyes. But when he did it, it was brilliant
"(But it) was a bit of sickener. I thought it was a blatant foul on James Tomkins, who is easily going to head the ball away. Wayne took him off his balance when he jumped, so he missed the header.
"Technically, in end the referee has made a big error as far as I'm concerned because the opposition has scored from that."
Allardyce also insisted that his side could have had a penalty for what he believed was a foul by Darren Fletcher on Kevin Nolan towards the end of the first half.
To add insult to injury, Manchester United's second goal came direct from the resulting counter-attack, as Rooney capitalised on Mark Noble's miscued clearance to side foot home.
Allardyce added: "We pushed and tried to get back into the game, and the game changes in split seconds.
"We could have had a penalty - the ball's come into the box, Kevin's looking to strike the ball at goal, Fletcher gets across him then they go right up the other end and Mark Noble mis-kicks his clearance and it goes to Wayne Rooney.
"So what could have been 1-1 turned out to be 2-0. It was a shame, it was defining moments that decide it, it went in their favour."
