The Welsh side headed to the King Power Stadium looking to extend a three-game unbeaten run at the expense of Leicester, who began the day in last place.
But they fell behind to a Leonardo Ulloa goal on 15 minutes and although Andy King didn't make the game safe for the hosts until the final minute, Swansea rarely looked like claiming anything from the meeting.
"We probably got out-fought today which I haven't said too many times this season," said Monk.
"There was a little bit more fight in them which earned them the right to win the game.
"We knew with the crowd and recent results that the intensity would be high in the first 20 minutes and we didn't really get to grips with it, which didn't allow us to get a foothold in the game."
Forced into a defensive reshuffle by the absence of the suspended Neil Taylor and the injured Kyle Naughton, the visitors were regularly troubled by a fired-up home side for whom the in-form Jamie Vardy was again impressive.
Going forward, meanwhile, Swansea created only one chance of note and it was squandered by Nelson Oliveira.
Making just his second start of the season as a replacement for the injured Bafetimbi Gomis, the on-loan Benfica man found himself clean through on goal, but his shot was deflected wide by Kasper Schmeichel.
"Nelson had a great chance and he did well to stay on his feet, but he probably should have scored," Monk said.
"If we had got a goal then, the atmosphere would have changed and that might have put a bit of nervousness into them.
"But these are the fine margins that you're dealing with at this level."
