The Canaries, who won thanks to Jonny Howson's goal, are second in the Championship with two wins from three.
"The first 10 minutes were quite even but after that we were in control of the game. We hit the woodwork a few times," Neil told BBC Radio Norfolk.
"If our passing in the final third was a bit slicker we would have had more chances. I think we deserved to win."
Neil continued: "I can't really remember too many opportunities for them to score, if any.
"The first goal is crucial because it mucks up their gameplan because they need to come out and leaves us more space to go and exploit."
Norwich were relegated from the Premier League last season with 67 goals conceded, the joint-second-most in the division.
But they have kept clean sheets in their last two home games, and Neil said: "That's going to be key going forward.
"(A lack of clean sheets) was a criticism of us last season and something we want to try to fix. In the last two games it's been better."
Norwich boss Alex Neil was pleased with his side's "control" during their 1-0 victory over Bristol City on Tuesday.