City only managed to score once in the first half, through Sergio Aguero, but managed to carve Norwich open in the second period and Mancini was happy with the perseverance showed by his players.
He told BBC Sport: "It was not easy because after the first half it was only 1-0 and if you don't score more goals, the game can change.
"I think after, we looked better but it was difficult because Norwich played with more players behind the ball and for us it was difficult in the first half.
"Sergio scored a fantastic goal though, it was not easy to score that goal."
Mancini was also impressed by the fifth goal, scored by Mario Balotelli, who shouldered the ball home after his initial effort was saved by Norwich keeper John Ruddy.
"Mario is like this," the Italian continued. "He is a fantastic player, he scored a fantastic goal.
"The goal he scored today was a good goal because he could only score like this."
The win saw Manchester City's 100% home start to the season continue and the former Inter boss is aware that his side will need to finish the season as well as they have started it if they are to win the Premier League this term.
He explained: "I think that it's not important to be there now but it is important to be there at the end of the season. We know that the season is very hard and very long.
"We don't know what can happen in the next month but it's better to stay top."
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