The Hammers had a legitimate early goal via Kevin Nolan disallowed for offside, while Yossi Benayoun hit the crossbar.
City increasingly dominated possession but could find no way through as the Hammers earned a valuable point in their push for Premier League safety.
Allardyce said: "I'm really pleased. 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."
Happy
Despite being pressed back into their own penalty area for long periods in the second half Allardyce was happy with the commitment shown by his players to pick up a good result.
He said: "In fairness to the lads, they kept on going and going. We had the odd breakout in the second half which caused them the odd problem or two and certainly Andy's (Carroll) overhead kick would've been a fabulous goal.
"It was goalbound. I don't know whether Harty (Joe Hart) would've saved it but it hit somebody else (Gael Clichy) in the back.
"But we have to be satisfied that we've taken a point off the champions and it really is a good day for us."
Allardyce also believes the display will give his players added confidence as they continue a tough run of fixtures leading up to Christmas.
The Hammers face Newcastle, Tottenham, Manchester United and Arsenal before the turn of the year but Allardyce feels they can head into what could prove a testing period with renewed vigour.
He said: "It gives us a lot of hope and I think a lot of confidence because it's a bit of icing on top of the cake for us today.
"We were disappointed we didn't get anything at Wigan and we've now got this huge, difficult fixture list that's coming up, Man City being the first.
"Of course, we played Arsenal a few weeks ago. That was, again, a difficult game, we had a lot more chances in that game than we had in this and actually lost the game.
"But this one is icing on top of the cake for us because it's a really tough group of fixtures and we've started by playing the champions of the Premier League and getting a point, so that gives us great confidence going on into this group of fixtures."
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