The Croatia international arrived from Rangers on transfer deadline day last January and scored 11 goals in 16 games.
Jelavic has only hit the net six times this season, but Moyes believes the player's work-rate will ensure the player finds his goal-touch soon.
"He has continually worked hard. I think probably the difference from this time last year is that everything we made Niki scored," said Moyes ahead of Wednesday's trip to Newcastle.
"This time we are finding it just a little bit harder to get the ball in the net, which was evident against Chelsea.
"You hope the players continue the form they have shown in the past and a bit of confidence can make a difference, especially to forward players.
"It is just the way it is, it happens sometimes."
Moyes admits he is having to become more creative in order to find ways to keep his side winning going into the second half of the season.
Injuries to key players - with midfielder Darron Gibson ruled out for a month with a thigh strain and forward Kevin Mirallas sidelined for a second time with a hamstring injury - have taken their toll over the festive period.
In Sunday's home defeat to Chelsea Moyes was forced to pick 18-year-old reserve-team defender Tyias Browning among his substitutes so limited were his options.
Things have improved slightly with the return from suspension of Marouane Fellaini and the possibility of Phil Neville being fit again after being rested having complained of pain in the knee he had an operation on recently.
But Moyes' management skills are being tested to the full once again and he accepts he may sometimes have to tinker with his tactics.
"The mood is fine, we are healthy enough - I'd like a few more players back from injury but so would a few clubs," he said.
"It is a busy time and I wouldn't say it is a time of year when managers and players want game after game.
"We've had them (Gibson and Mirallas) out before. Kevin and Darron are important players for us but that is what happens.
"It is a test to try to find teams that can win without your best players. You have to find solutions."
One of the changes which looked like paying off against Chelsea was moving Steven Pienaar into a central position behind Jelavic from where he scored in only the second minute.
The South Africa international is usually a permanent fixture on the left, where he has a great relationship with defender Leighton Baines, but in Fellaini's absence Moyes wanted to change things around somewhat.
"I don't think his biggest thing is scoring goals but we've needed to get some goals from different places and he's managed to get some in recent games which have been important for us," said Moyes of Pienaar.
"I don't want it to become predictable about Pienaar and Baines down the left and I felt it was right we changed it and I think he can do a job for us there.
"We will look to change it around when we can but we know we have a good thing going with what Baines and Pienaar do so we have to make sure teams don't clamp onto it too often and we can cause them problems in other ways."