Wilfried Bony's penalty in injury time at the end of Saturday's Premier League clash earned all three points for the Swans after the big striker had earlier cancelled out Shola Ameobi's opener for Newcastle.
The win at St James' Park lifts Swansea six points clear of the drop zone and Monk believes his side deserved to take all three points.
"It means everything," Monk told Sky Sports. "Three points was the ultimate goal for ourselves. We came up here with that belief to try and get those three points.
"It was never going to be easy against a Newcastle side in front of their own fans but we stuck in there. We started well - obviously the goal went against us, but we got one back just at the right time before half-time.
"In the second half we really stepped up, passed the ball a lot better and got control a bit more and thankfully we got the deserved penalty at the end.
"We had a chance just before that [the penalty] with Bony, where he was through on goal and the keeper read what he was trying to do and you kind of think that is the chance gone, but we stuck in there.
"They threw a lot at us and we defended well second half and really dug in and we got our just rewards with the penalty - a stonewall penalty. I don't think anyone can have any complaints about that, and the all-important three points."
Monk also hailed Bony as he made it 22 goals for Swansea this season with his brace on Tyneside.
"Yeah, his impact has been massive," added the Swans boss, "not just with his goals, but the way he has been amongst the group.
"He is a really good character. He works hard every day in training, he is pushing other people and he is pushing himself and they are the type of people you want to work with and the type of people you want in your team. He can offer so much more and he really deserves that."
Monk also felt the performance was the perfect response to the club's critics after reports emerged of a training ground bust-up prior to last weekend's home defeat to Chelsea.
"I think we proved that last week with the Chelsea performance going down to 10 men in such an early period we dug in and we showed the same spirit as we showed today so I think you can see the squad is unified and that we are all together which is important," concluded Monk.