The Swans head to Everton on Saturday, standing just four points above the drop zone.
They have not posted a league win since beating Cardiff almost six weeks ago, with last Saturday's 2-1 home defeat against West Brom leaving them still within striking distance of the bottom three clubs.
"The good thing for us is it's in our hands," Monk said. "We are not chasing to try and make up points. It is upon us to make sure we fight for every single point.
"I have got no question over the players. They all want to do well. Their attitude has been spot on.
"At the end of the day, they realise what is at stake. When you get questioned, you tend to get a reaction.
"Everyone always talks about the 40-point (safety) mark, but a lot of the teams have to play each other. A lot will drop points and a lot will get points.
"The reaction this week has been very good. You have to be honest with people. I told them straight after the game (against West Brom) what I felt. They are all in it together and pushing each other.
"I am more than confident that in the coming games we will earn enough points to achieve what we want to achieve."
Swansea were boosted against West Brom by Spanish striker Michu's return off the bench following a 17-game injury absence, and his record as a proven top-flight goalscorer could ultimately be a decisive factor in steering his club to safety.
"He hasn't had a lot of game time," Monk added.
"It is about building him up, really. Whether he starts or not on the weekend, we haven't decided.
"It is unfair to put too much pressure on him. Of course, he has got the quality to score goals for us, and he is a very important player with the quality he has got, but it is important we don't rush him."
Jonjo Shelvey and Nathan Dyer are set to join Michu in being part of the squad for Goodison Park.
Shelvey has been out for almost a month with hamstring trouble, while Dyer missed the West Brom game due to a heel injury.
Swansea, who were knocked out of the FA Cup by Everton earlier this season, have never beaten the Merseyside club, and Saturday's clash sees a quickfire return appointment with their former manager Roberto Martinez.
"They are very strong at home," Monk said. "They are pushing well in the league. We played them in the cup not long ago, and for 60 minutes our gameplan worked very well.
"We realise how hard it will be, but we will go up there with a determination to try and get a reaction from last weekend.
"Roberto is a good manager. From his time here, you could tell he was always going to go on and do some good things in football. He has got his chance now at Everton, and he has taken it very well."