Two goals: Patrick Vieira (centre) was the unlikely hero as Man City knocked out Notts County
Vieira's double was key as City laboured against League One side Notts County before late goals from Carlos Tevez, Edin Dzeko and Micah Richards completed a flattering 5-0 win.
The former France midfielder said: 'We know how to win but we saw how difficult it will be to go all the way.
'We need to believe in ourselves, work as hard as we did today and we will see.
'It's a competition in which the club want to do well. It's important for us to win some silverware this season but there is still a long way to go.
'But when you see how deep our squad is we have to believe in ourselves.'
Both Vieira's goals came from corners and the former France international admitted the team should score more from set-pieces.
He added: 'We don't score enough goals from corners or free-kicks so thank God I scored twice.
'We have to give them credit for the way they played in the first 20 minutes, they put us in trouble.
'We are happy to get into the next round.'
City will face Everton or Reading in the quarter finals if they beat Aston Villa in the fifth round.
Manchester City 5 Notts County 0: Vieira at the double as Blues run riot FA CUP QUARTER-FINAL DRAW: United set to face rivals Arsenal Man City forced to wait on crocked midfielder Johnson's comebackAll the latest Man City news, features and opinion
Explore more:People: Carlos Tevez, Edin Dzeko, Patrick Vieira Places: France