Sergio Aguero opened the scoring early in the first half before putting the visitors further ahead six minutes after half-time.
The Hammers put in an improved second-half performance but that was of little consolation to Allardyce.
"It was too late, though, wasn't it? That was the problem," Allardyce said.
"Manchester City were better than we were.
"I have always said if you are going to get a good result then you have to play your very, very best and sometimes the opposition don't allow you to do that.
"I think that we thought we could come out of the traps and set the tempo, but what happened was that Manchester City decided they would do that because of their quality.
"When you get the front two and Yaya Toure and Silva passing the ball like they pass it, it frightened us a little it, it put us on the back foot.
"The sad thing was that even after that, we made two basic errors for their two goals rather than the quality of Aguero or Alvaro Negredo or Silva putting the ball in the back of the net with a great fluent move."
Allardyce continued: "A simple ball down the middle for the first goal and somebody not picking up the smallest Man City player up for the second goal was really disappointing for us.
"Gifting them the two goals was something that you wouldn't expect to come back from against a team of their quality.
"But we gave it a go, I was pleased with the response. At least they didn't give up, they fought to the end and when we got to 2-1 with a good goal that we scored.
"We showed a little bit more of our passing qualities, which failed us in the first half.
"The constant passing to our players, and then the opposition regaining possession was the reason why we didn't look anything like we did at Tottenham.
"Really, our only real contribution from an attacking point of view was about 20 or 25 minutes from the end after Man City were 2-0 and that was too late."