Substitute Lambert struck in the third minute of stoppage time after Swans skipper Ashley Williams and goalkeeper Michel Vorm got themselves in a tangle.
Williams' attempted clearance ballooned high in the air, dipping behind a retreating Vorm, and as all three players scrambled for the ball, it appeared to go in off Lambert's back.
"The last home game of the season and we lose the game in the last minute
It's always hard to take," head coach Monk said.
"We suffered first half, possession-wise, playing against a very good team in Southampton
They worked their possession well.
"But we had three really clear-cut chances we should have scored from
I can't actually remember Michel Vorm making a save the whole game.
"In terms of possession, we suffered, but I think second half we got to grips with it a little bit better and we had the best chances
How we have come away from that game with nothing is hard to take.
"But I've said that a few times this season
It has pretty much been the story of our season
There was some very good defending for 90 minutes, then we let ourselves down with some schoolboy defending.
"We should be scoring from those clear-cut chances and we left ourselves open for the sucker punch, which we've done a few times this season."
It looked as though the teams would play out an uninspiring 0-0 draw in the Liberty Stadium sunshine after 90 minutes that had end of season stamped all over them.
With neither Swansea nor Southampton troubled by matters at the top or bottom of the table, it was a contest that drifted along with no obvious urgency, and Lambert's goal provided an ending the match scarcely deserved.
Despite the defeat, though, it is likely that Monk will be upgraded as Michael Laudrup's permanent managerial successor during the next week.
Monk has achieved the primary aim of masterminding Swansea's top-flight status for another season and after the club's directors met on Friday, it would appear they have been suitably impressed to let him take the Swans forward.
"If you look at the effort and commitment from the players, you can't fault them," Monk added.
"For 90 minutes, they defended the box extremely well, and that takes intensity and concentration to be able to do that.
"But it was a poor goal
We got ourselves out of our shape
We lost concentration, got sucked out of position, left Lambert with too much space, and indecision from the recovery side cost us.
"We didn't deserve for it to go against us, but it has happened."
Southampton manager Mauricio Pochettino started with Lambert on the bench after he suffered a knock during last Saturday's 2-0 victory over Everton.
"He received a knock in the game against Everton, and he wasn't able to train properly throughout the week," Pochettino said.
"He wasn't fit enough to play the full 90 minutes, so we thought we would put him on the bench and bring him on in the second half
We didn't want to take any risks with him.
"In the history of football there have been more bizarre goals than that one, but I guess it can happen in the world of football.
"I thought that overall we did very well
We are very happy with the victory we achieved, and with the team's performance.
"It was sort of a difficult game to play
Both clubs had already achieved their goals for the season.
"Mathematically, we couldn't go higher than eighth, but overall we played with a lot of intensity and in the manner that we know how to play.
"Perhaps it wasn't a spectacular game, but we did achieve the three points which helped us achieve the highest number of points that we have ever achieved in a Premier League season, and also the number of wins away from home, so for us these three points are massive."
Source : PA
Source: PA