The former Real Madrid boss replaced Steve McClaren this month but suffered defeat to Leicester City in his first match before drawing with Sam Allardyce's side on Sunday.
Newcastle are three points from safety with eight matches to play, but Mannone believes Benitez faces a huge task to steer them away from the drop zone given how late into the season he has taken charge,
"They still had the problems in the first hour of the game [on Sunday], we saw that," he said. "So I don't see how the new manager can sort everything out in the next eight games. It will be hard.
"It is difficult when a manager comes in for the last two months. It is not easy. I have seen it myself in the last couple of years.
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"Benitez is a top manager. He has been at some good clubs. It will help Newcastle to have him. But we have to look at ourselves."
Norwich City, lying in 17th place, face both Newcastle and Sunderland after the international break, and Mannone has underlined those fixtures as key.
"We all play each other in a few weeks when we both go to Norwich," he said.
"We have to seize our chances before we meet them. We have West Brom and Leicester at home so we have to take the chances before we go to Norwich.
"I am confident we can get out of it. The team has improved a lot. We look more solid. We create chances, scoring goals but we are still missing that edge to not concede.
"I am trying to do the best I can to not concede and I think we are all putting our foot in to help this club survive."