Having seen a couple of their top flight rivals come undone earlier in the fourth round of the FA Cup, City avoided the same fate after racing to a 2-0 lead at the break courtesy of Yaya Toure's opener and a controversial Sergio Aguero penalty, before wrapping the tie up with second-half strikes from Carlos Tevez and Aguero.
The comfortable win over their Championship opponents came as a timely boost given their recent league woes and, after watching Aguero take his tally of goals in a stop-start season to 13, the Italian predicted twists and turns if his men can start scoring on a regular basis again.
"I hope Sergio will be like this from now until the end," said Mancini. "Because if Sergio is like this, and our strikers continue to score a lot of goals from now until the end, I think the championship is not finished.
"This is possible but I think it should be confident, always. If we are 12 points behind - we lost seven points in three games. This can happen for every team. We play a lot of games.
"I think in this moment they [league leaders Manchester United] deserve to be there because they played better than us. They scored more goals than us."
On a weekend which saw Arsenal lose 1-0 at home to Blackburn, while Everton drew 2-2 at Oldham, the conquerors of Liverpool in the last round, Mancini was glad his side prgress to the fifth round of the competition.
"It was important to win this game," he added. "Clearly if you score two goals in the first 20 minutes it is easier.
"The FA Cup is a difficult competition. Every team plays like the Champions League final. For this reason the FA Cup is an important trophy in England, because you should play 100 per cent if you want to win.
"Arsenal yesterday [Saturday], Everton, other teams that play in the Premier League that went out of the competition ... if you don't play with full concentration it is difficult.
"We started well with good intensity, we were concentrated on this target and after that we scored four goals."
Mancini did not feel the awarding of the controversial penalty that led to Aguero's first goal was relevant in such a one-sided game.
He added: "The game has finished 4-0 and I don't think we conceded a lot of chances. I think the result is correct but I don't know if it was a penalty."
Part of City's problem this season has been a glut of injuries with various players, Aguero included, picking up niggles here and there. Gareth Barry missed Sunday's FA Cup tie with an ankle problem and captain Vincent Kompany has a knee injury.
"For this we are unlucky this year. Gareth was nothing. I think he will be ready. We hope we can recover Vinny for the next game. Javi [Garcia] we will see tomorrow [Monday] or Tuesday. I don't think that is a big problem, Mancini said.
Manchester City will face a tough test back in the Premier League next Sunday when host Chelsea at the Etihad Stadium