The Swansea head coach has seen his side fail to win in the last four Premier League matches, including surrendering a lead in last weekend's 2-1 defeat to West Brom at the Liberty Stadium.
That poor run has left Swansea in 14th position and just four points above the relegation zone, with nine games still to play.
Monk is anticipating a nervy end to the campaign for several sides who are mired in relegation trouble, but the 35-year-old is confident that his charges will pick up enough points to beat the drop.
"It's very close and intense," Monk said. "The good thing for us is that it's in our own hands, we're not chasing to make up points. But we need to get those points as quickly as possible to make us safe.
"I'm totally confident we'll earn enough points to be okay, we're talking about two 45-minute periods where we haven't performed like we should have.
"The attitude has been spot on, they realise what's at stake - and once you get questioned you tend to get a reaction. A lot of teams have to play each other, a lot will drop points and make points."
Swansea have the chance to bounce back from the West Brom disappointment in Saturday's visit to Everton.
Monk has been happy with the way his squad have performed in training this week, but is keen for that to be turned into three points.
He added: "The reaction in training this week has been good and all the players have been pushing each other.
"But the ultimate point is you've got to turn those performances into results. If I'm not happy I'll tell them but they weren't happy themselves (after the West Brom loss).
"We have spoken a lot this week and shown them things we need to improve on, but the key is that we've got a group who want to do well and get out of this situation as quickly as possible."
