Benitez, a Champions League winner with Liverpool in 2004, replaced Steve McLaren at St James' Park earlier in the month, having been sacked by Real Madrid in January.
The Spaniard started his reign in the North East with a loss to log leaders Leicester City and a draw with derby rivals Sunderland.
"We have a top-class manager now. We have to believe he can get us to stay in the Premier League," Janmaat said in the Daily Mail.
"He has had a positive effect. It has been organised, the way we played at Leicester and against Sunderland. We have to keep doing that and looking up.
"We feel we can stay in the Premier League, but know we need more wins. We hope and we have the confidence. We must still believe and go out looking to get the job done. I think we can do it."
The Magpies are second-from-bottom on the Premier League table with 25 points from 30 games - a point behind Sunderland and three shy of their next opponents Norwich. The Canaries are hovering just above the drop zone and have played an extra match.