The Villans secured their place in the top flight for another season as they eased past the Tigers at Villa Park.
While there has been some trepidation around the club in recent weeks, Lambert believes that the supporters were "excellent" in helping the players claim the points yesterday afternoon.
"[The fans] were excellent but I had a feeling they would be," the Scot is quoted as saying by Sky Sports News. "They played a huge part in our win.
"It is a big, big club with a massive fan base and you've got to give them something. I knew this was going to be a hard game but I thought we were excellent. They came with great enthusiasm for the game. They were fantastic."
Villa return to Premier League action on Wednesday when they travel to title-chasing Manchester City.