Victory for Villa on home soil all but ensured they will remain in the top flight next season, despite a worrying run of form in recent weeks.
Lambert's men are now six points clear of his former club Norwich City, who have two games to play and a vastly inferior goal difference.
The Scot paid tribute to Villa's fans after the game and is already looking ahead to Wednesday's game at title-chasing Manchester City.
"We could sense when we came off the team bus that the fans were going to be right behind them," Lambert said.
"I've said it before - it's a massive club with a massive fanbase that won't accept too many defeats.
"We've had too many, especially here, but when you see a performance like that I'm pretty sure they'll be delighted.
"We'll go and do our utmost to try and win games. (On Wednesday) we're going up against a team who could win the league.
"They're one of the best in Europe but we'll go there and try and win and try and stop them. I know it's going to be a hard game against a top team."
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