Jelavic, short of confidence, turned in a good shift in victory against Fulham.
"He knows. And the crowd are desperate for him to do well you can tell," said Moyes. "There's other players who would maybe get criticised but they don't (with him) because they know how well he has done and what he is capable of.
"And everybody is urging him and saying 'Come on then, let's get these goals and get underway again'. And that's the way we've felt about it all year. He's been great with his work.
"He's been the first one to accept that he needs to do better and I think when you have people like that it gives you a chance of getting better and the improving."