Hart has come in for criticism for the gaffe he made against West Ham last weekend when he let Andy Carroll's last-minute shot slip through his legs.
The England No.1 is on course to win the Golden Glove award for the most clean sheets in the Premier League for a third successive season and Lescott admits Hart will bounce back from his error against West Ham.
"The goal against West Ham was down to his back spasm," Lescott told the Daily Mirror.
"Obviously he was disappointed to concede and, knowing Joe, he'll be gutted for a week now.
"It was one of those things but we have no qualms with Joe at all, at any stage of the season.
"If he made an error, or what he sees as an error, we still won the game 2-1.
"Joe will play it down but I know he really beats himself up about these things.
"He's on course for the Golden Glove again and he prides himself on that.
"He's got 15 clean sheets this season and I know that award means a lot to him.
"He'll just get his head down in training and try and better himself as he does every week."