The Croatian was on fire when he first joined the Toffees from Rangers a year ago, finding the net nine times in 13 appearances.
However, he has struggled to replicate that form this season, returning with just six in 22 starts.
Victor Anichebe was instead chosen to lead the attack against the Baggies, with Moyes revealing that he wanted to take some of the pressure off Jelavic.
"It's something I had been considering for a while," Moyes told reporters. "I wanted to give [Jelavic] every opportunity to get goals but it didn't quite happen.
"It was something I was reluctant to do but I felt in the end that it was right to give him a breather. I actually thought Victor did well in the game; he offered us something different.
"Hopefully we will get Jela back to form, that's the key to it all."
Jelavic is expected to start today's home fixture with Aston Villa.