The Croatia international has not scored in his past nine appearances and his only strike since December 9 came against League Two Cheltenham in the FA Cup.
Such lack of form contrasts sharply with almost 12 months ago when the 27-year-old enjoyed a run of 11 goals in 14 matches to the end of the campaign which had many hailing him as the buy of the January window at a cost of just £5.5million.
It has cost him his place in the starting line-up recently and while Moyes accepts the player's confidence has been dealt a blow he is backing the forward to bounce back.
"I am not that cuddly a fella or one for putting my arm around you all the time but every manager has their own style," Moyes said.
"I don't know if Jela is the sort of boy who would want me to do that any way.
"Any forward who has played the game and been through barren spells will tell you they practise more or don't do any in the hope it comes back without it.
"I think it is every man for themselves in that. We would like him to get his goals and lift his performances and if we get that it will be a big help to the team.
"The team need him. I said last week a lot of what we do this year will be determined by how well Jela scores between now and the end of the season.
"It is noticeable (his lack of goals) because everyone talks about it.
"We tend to be as honest as we can and not hide away from anything and at the moment undoubtedly we need Jela to find a way of scoring some goals.
"He needs to get a goal but I don't know if one goal will make everything right.
"If I saw him getting four goals in four games then I would start to think 'This is what we want'.
"You have to find a way of making that happen again but we could do with him standing up and getting us some goals now."
Of the top eight only West Brom have scored fewer goals than sixth-placed Everton.
Moyes knows it has lost them ground on the race for Champions League qualification as their failings up front have led to concessions at the other end proving more costly - as their 12 draws this season highlight.
"We are disappointed we have not scored more goals - if we had maybe the boys at the back would not have had so much to deal with late on," said the Scot.
"Our play in between the boxes has been very good but we need to do a little bit better in the boxes because, to be fair, that is where it really matters."
Jelavic's goal drought has been compounded by the unavailability of forward Kevin Mirallas, who began his first season at the club brightly but has been hampered by a recurring hamstring injury.
The Belgian scored in the midweek FA Cup fifth-round replay victory over Oldham and Moyes hopes that may help re-ignite his season.
"His first two or three games back were a gentle introduction and we hope he kicks on now after the goal as he looked a bit sharper in his general play the other night," added the Toffees boss.
"We are hoping we can get a bit more from Kevin because he was a big goalscorer in Greece (having signed from Olympiacos in the summer).
"A lot of our players have settled in quickly - Jelavic did incredibly quickly - and although Kevin started the season well I think he is still coming to terms with the Premier League.
"I am hoping the last 10 or 12 games he can help us as it is his job to score goals with Jelavic, Victor Anichebe, everyone."