The east London club have now kept four clean sheets this term, an improvement from results such as away defeats to Wigan and Swansea. However, the defender, who has started every league game, feels the club have improved throughout the season and deserved the point against Roberto Mancini's team.
The Hammers' defence faced £120 million worth of strikers on Saturday evening, as Edin Dzeko, Mario Balotelli, Sergio Aguero and former West Ham striker Carlos Tevez all took to the field at some stage in the game.
"We were good but we knew we had to do it at home because, by our standards, we were poor last week at Wigan," Collins told the club's official website.
"Especially with the run of games coming up, we knew we had to come and play well and defend well and we have done that.
"Certainly in the second half we were camped on the edge of our box for long periods but that's what you have got to do against such a quality team. You know you are going to have to defend and not make mistakes. I think we did both of those things well."
Collins joined the Hammers from Aston Villa in the summer for an undisclosed fee, and has since gone on to establish himself as a regular for manager Sam Allardyce.
"My performance was about right for me - I head it, kick it and block it! I'm happy. We're keeping clean sheets and defending well apart from a few games when we've been a bit slack and not on our game. Overall we've defended well as a team this season.
"In games gone by we have gone out all guns blazing and chasing and chasing to try to close the other team down and win the ball back, but on Saturday the boss played it perfectly. We sat back let them play in front of us and then nicked the ball off them and went on the break - I think it worked perfectly."West Ham have a tough set of fixtures in the next four weeks including away visits to Manchester United, Newcastle and Tottenham, as well as home matches against Liverpool and Chelsea.