Wilfried Bony's stoppage-time penalty secured a precious 2-1 victory for Monk's team that puts them on the verge of Premier League safety, following a week in which another training ground bust-up has fuelled more reports of disharmony at the club.
Shola Ameobi opened the scoring for Newcastle, who have now lost five games in a row, but Bony equalised with a towering header just before half-time and then won it from the spot after Marvin Emnes was upended by Cheick Tiote.
Monk, who was involved in a training ground spat with Chico Flores before he took over as coach in February, described this week's incident as "handbags" before the trip to St James' Park.
And the 35-year-old pointed to Saturday's victory as evidence that his players are united.
He said: "If our squad wasn't together you wouldn't get a performance like that and you wouldn't get a performance like we did against Chelsea (in a 1-0 defeat last weekend), when we went down to 10 men after 16 minutes.
"It's clear to see the players are together and they're fighting for the club."
When asked if the reports of unrest had made his job easier, he added: "It can do, especially when it's fabricated so much.
"It just galvanises you a little bit and that's what you have to use as a manager and also as players. I don't think we needed that anyway, we were ready to go for this game and the last game."
Swansea are now six points clear of the relegation zone with three games remaining, but Monk will not accept they are safe just yet.
"It was a relief to get the three points," he said.
"Whether it's enough I don't know, but I don't really look at it like that. I just look at it as we've got three more games to go and nine points to play for and we want those nine points.
"We've played a lot better than we did today and got nothing. But right now at this stage of the season it's about getting the job done and whichever way that is, you take it."
