Jelavic grabbed a dramatic winner with only his second goal since the start of October, just seconds after Steven Pienaar had hauled Everton level with a 90th-minute header.
"I thought it was a great finish by Nikita, and it can only do him good," said the Everton manager. "To be alert and alive to the situation and finish first time like that was excellent.
"There has been some frustration in his play in recent weeks, but he has been getting closer to his true level.
"A win like this can give you a real lift and make a huge difference to your season. It shows the belief and persistence among the players. I thought they showed great character.
"It was as good a finish to a game as we have had for some time. We have been on the end of a few lately that have gone against us, so we were due one in our favour.
"If we hadn’t won, I would have been asking why not, because I thought our play was terrific, especially in the first half. It is a bit early to be talking about Europe, but where we are in the table does not shame us or the way we have been playing one bit."