Substitute Lambert struck in the third minute of stoppage time, his 12th Premier League goal of the season, 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.
“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.”
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 former Saints defender Monk will be upgraded as Michael Laudrup's permanent managerial successor during the next week.