Mancini insists West Ham didn't deserve their point from yesterday's 0-0 draw.
Allardyce disagreed with Mancini's take on the result and felt his team were good value for their point.
"I'm really pleased," he said. "I think that our performance today from start to finish was very, very good indeed.
"The way we started the game was bright, trying to see if we could test Man City early on.
"Of course, we did that with a fantastically-taken goal by Kevin Nolan that I think was a little unfortunate to be given offside.
"But the first half, we tried the best we possibly could to put more and more pressure on Man City.
"Of course we would have to do some severe defending somewhere along the line and that wasn't so much in the first half but certainly was in the second."