The Italian replaced the injured Keiren Westwood for the defeat at the KC Stadium and held onto his starting spot for the Capital One Cup clash with Southampton.
The 25-year-old arrived at the Stadium of Light from Arsenal during the close-season for an undisclosed fee after making just 26 appearances for Arsene Wenger's side in eight years.
Sunderland face Manchester City on Sunday and Mannone is determined to win the battle with Westwood for a place in Gus Poyet's side.
"Of course I want to keep my place, that's why I came here," told the Shields Gazzette. "I've been hurting on the sidelines, so I was really happy to take my chance on Saturday and do well for the team.
"It was a really good win [against Southampton], and I was involved in a good performance. I want to push on.
"Obviously it's down to the manager, but I'm available for him, and I will push as hard as I can in every single training session, and every single chance I get out there.
"This manager is very open to performances, he likes to watch the game, and he will pick what he thinks is the best side.
"Hopefully I've done enough to show I can play in this team, and I want to push on to be number one."