Sunday's 1-1 draw with Crystal Palace at the Liberty Stadium was the Swans' seventh match in 22 days and left them five points above the relegation zone in 14th place.
Monk's men are now having three days off before getting back to work ahead of their next game - at home to West Brom on March 15 - and the player-manager feels the break has come at an ideal time.
"The players need it," the 34-year-old said. "But I think they're at a level now where they can have the few days' rest that we're going to give them and then be ready to work and all focus onto West Brom."
After a dominant first half in which Jonathan de Guzman put them in front, Swansea faded badly.
Chico Flores was sent off after bringing down substitute striker Glenn Murray late on. The offence appeared to take place just outside the box, but referee Mike Dean pointed to the spot and Murray duly converted.
Monk nevertheless remained upbeat about his team's chances of securing another season in the top flight.
"We will be fine," he said. "If they continue to show that commitment, that appetite to win games - now with the rest we can get in between and the work we can now do with the players in terms of preparation - they'll be fine.
"But nothing's ever given to you in football. You have to earn it, and they know that."
Monk described some of his side's recent performances as "phenomenal", even though they have gone half a dozen games without a win.
"Of course you get frustrated because you're not getting what you deserve," he said. "It's human nature, isn't it?
"But I think they're enjoying themselves in terms of the way they're trying to play football and trying to win games, and the mentality they're taking into every single game.
"Obviously, when you put that amount of physical output into a game and don't get the rewards that you deserve, it is hard to take."
Full-back Angel Rangel shares his manager's confidence, having noticed a healthy "arrogance" on the pitch since Monk took over from Michael Laudrup four weeks ago.
"We know that with recharged batteries we will be fit for the remaining 10 games and hopefully we'll get as many wins as possible," the Spaniard said.
"You can say that the tempo of our game is a lot higher. We are going back to the Swansea way, I would say, and obviously we were missing that.
"The results haven't been great for us, but when you play good games obviously the results are going to come. We are confident and we do believe we can achieve it.
"I think we've played over 40 games already now and the last 10 games are going to physically and mentally be hard for us, but we've always shown that, when we're under pressure and we need wins, we get them.
"Now is the moment that we have to show that we're a good team. We want to stay up, so we've got no choice really. We have to give everything until the end and I think we've got enough arrogance and quality to stay up."