An 84th-minute penalty from Christian Benteke appeared to have won the day for the visitors but Danny Graham struck four minutes into stoppage-time to earn Swansea a point.
Lambert, who had received plenty of flak with his side conceding 15 goals in the previous three games, said: "I don't think it's two points dropped, I think it's a huge point for the football club. Today showed me that these players are mentally very strong. A lot of teams go away from here with nothing."
The hosts should have gone ahead inside three minutes when Wayne Routledge found himself alone with only Brad Guzan to beat. Guzan somehow clawed Routledge's shot to safety before beating away Graham's point-blank strike from the rebound.
There was no mistake from Routledge five minutes later as Villa were once again undone. A crisp through ball from Pablo Hernandez caught the visitors off guard and though Guzan spread himself, Routledge dropped his shoulder and rolled the ball into an empty net.
Michu struck the post a minute later as Villa were once again torn open. After Graham's shot had been caught by Guzan, Michu executed a wonderful turn on the edge of the Villa box before striking the upright for the second time in the game.
With Villa on the ropes, Swansea paid the price for their indecision in front of goal. Ashley Williams failed to clear on the edge of the penalty area and Andreas Weimann beat Michel Vorm from 18 yards to set up the late drama. (© Daily Telegraph, London)