Sunderland, who are only out of the bottom three on goal difference, have three games left to play before their season is over.
"We cannot assume that we have achieved anything," The Mirror quotes Mannone as saying. "Nothing has been done yet, we have just started the job.
"Before the Cardiff game, we had four games to go, and we talked about how they were four finals for us. We've only won one.
"There are still three more to go and they are every bit as important, if not even more. We have only won one battle. To win the war, you need to succeed in another few fights."
Sunderland's next fixture is away to Manchester United on Saturday.