The Black Cats' next three Premier League fixtures will see them travel to Manchester City, Arsenal and Liverpool.
They also face a home date with Southampton in the FA Cup fifth round and a Capital One Cup final date with Manchester City at Wembley.
It could be that the next few weeks make or break Sunderland's season, with Gus Poyet's side having dropped back to within a point of the relegation zone, but Mannone believes they have already shown that they are ready to face their challenges head on.
He told the Sunderland Echo: "We are in a situation where we need to win games or at least draw them.
"We are going to big, big clubs, but we have to fight.
"We came back from a situation where everybody was thinking we were relegated and dead, and we've put ourselves in a situation where we can fight. That's what we need to do again.
"Any game in front of us is an important one to get points from and we will try our best. We're not fearing anybody and that's the mentality.
"It will be a test at Man City (on Wednesday), but a good one for us, even if they are really strong at home.
"Everybody agrees they are scoring goals for fun and we will need to be at our best to defend really well and do something attacking.
"It's going to be a tough game, but it will put something in our minds of what we're going to do in the final."