Roberto Mancini says that it is "not a problem" for Manchester City to overcome the seven-point lead forged by Manchester United in order to defend their Premier League title. "Last year we covered five points in two [three] games, this is not a problem," said Mancini after a thrilling victory over Norwich on Saturday, despite going down to 10 men shortly before half-time.

It was a performance that prompted Mancini to reassert his faith in the team following a 1-0 defeat to Sunderland on Boxing Day that had rumour mills whirring of a crisis in the City camp. "Sunderland was disappointing only because we were missing a goal," said Mancini of a match after which some of his players confessed to their anger in the dressing room.

"When you go away and have 70% of the possession, 24 chances to score, you can't lose a game, never. I was disappointed but if you play like today, you have the same attitude, I think that the season could be very important for us."

Before facing Norwich, City held the tightest defence record for away games in the league; two sloppy concessions and a free-kick put paid to that but Mancini waved away any concerns over his back line. "No, no, no, no I was happy with the defending because [we were playing] with 10 players for 60 minutes – 60 because we got seven minutes extra time. I think that we conceded the second goal because we did not mark. There we should have paid more attention but after I was happy because to defend today was difficult.

"Yes we were one of the best defences in the Premier League, today we conceded three goals – one free-kick that was not a free-kick, the other two came when we were with 10 players. When we are with all the players this season they [the opposition] don't score against us."

City's form has raised serious questions over their ability to win a second successive title – before Saturday's thriller at Carrow Road, Mancini's team were averaging a goal a game less than last season. Sergio Agüero's and Edin Dzeko's returns at the midway point are almost half their hauls at the same point in 2011-12 but the victory against Norwich seems to have reaffirmed self-belief within the side.

Dzeko, who put City 2-0 up after four minutes, echoed his manager in the context of the title race. "It's everything open," said the striker, who insists he is claiming a hat-trick against Norwich, despite his third effort being recorded as a Mark Bunn own goal, "so many games to play and nothing is finished. We will fight to the end."

Chris Hughton's side visit West Ham on New Year's Day. The London club are one place below Norwich – 12th – in the table and over the summer had attempted to lure striker Grant Holt to the capital. "I'm very pleased we kept hold of him," said the Norwich manager, who has yet to learn whether the 31-year-old will be fit. "We need him back and available in the squad."

Norwich have lost three games on the trot but Hughton is thankful for the 10-game unbeaten run in the league that preceded the Christmas fixture list.

"It makes you grateful for that run, which I think in this division was a wonderful achievement," he said. "But certainly if you'd said to me earlier in the season would I be happy with the points tally we've got I would have said yes, but it's very much now about getting back into good form and to start picking up points again."

Man of the match Edin Dzeko (Manchester City)