The striker failed to make the squad for last week's 1-1 draw at Leicester.
Berahino hasn't scored in 733 days and his place on the bench went to 18-year-old debutant Tyrese Campbell at the King Power with Peter Crouch injured.
Lambert said: “He's not up to my level of fitness. He's a fit lad but there's got to be more to it and that's what he's got to work on.
“He needs more fitness to his game to play the way I want him to play. I don't think he's up to the levels he should be.
“I have told him that, so he knows. But it has to come from him as well.
“In the situation we're in we need everybody to put their shoulder to the wheel and be able to get around. That's important."