The Blues had surrendered a 1-0 lead late on but responded well, netting the winner courtesy of a Yaya Toure penalty.
Speaking in his post-match press conference, the Chilean asserted City were worthy of the three points, but admitted they had to dig deep to achieve them.
“I think we deserved to win the game,” he reflected. “We started from the beginning to try and score.
“Norwich played very well because they defended very well with 11 players near their box.
“It was very difficult for us to create space but we created three or four chances that we missed.
“Finally, we opened the scoring with a beautiful goal from Nicolas Otamendi.
“Unfortunately, they drew level with a very unlucky goal but in the last ten minutes, the team demonstrated its personality and character.
“We believe in what we can do and we went on to score what was a clear penalty and then miss another.”
On the subject of Norwich’s equaliser, Pellegrini refused to lay blame on goalkeeper Joe Hart or admit disappointment in him.
City and England’s number one was at fault, dropping a looping cross into the path of Cameron Jerome, but redeemed himself with a stunning, crucial save in injury time to thwart Jonny Howson’s deflected effort.
When asked about the Canaries’ leveller, Pellegrini told press: “It was unfortunate. Sometimes, these things happen. Joe is human and he can make mistakes.
“Apart from that error, there were only two shots at him in the game and he saved those because he is a very good goalkeeper.
“We played against a difficult team that played very well.”
