Striker impresses in first Premier League start
The Canaries produced a determined display to keep the visitors at bay throughout the contest, while Bamford himself went close to scoring when his first half drive from distance slammed off the crossbar.
"We all needed this after good performances in the last few games," the striker told Norwich City TV.
"The point helps us turn things around, particularly coming against a big team like Manchester City. I think it will do that, because it was a great performance from every single player in the team.
"Everyone put a massive shift in and they deserve credit for that. We had a game-plan to try and give players like David Silva and Sergio Aguero as little time as possible, and you could see the energy we put in.
"It's a massive result for us but now we'll move onto next week with positive thoughts. We want to use this to build some momentum."
Having been handed his first City start by Alex Neil, the 22-year-old added: "I'm thankful to the manager for giving me the chance.
"Now it's up to me to start paying that faith back through goals. When I first hit my half-volley I thought it was going in, but then it kept rising so wasn't to be.
"It's been easy for me to settle into the group, especially having come up against a lot of our players last year. That's helped me, and now I want to help keep this Club in the Premier League.
"I feel like I had a good 60 or 65 minutes and hopefully I can build on that."