Jelavic scored the only goal of Saturday's game at Goodison Park - his first for the club on his full debut - but he was one of several key players left out for Tuesday's Merseyside derby defeat at Anfield.
The Croatia international was on the bench along with Tim Cahill, Phil Neville, Royston Drenthe and Leon Osman and could only look on as Liverpool won the match 3-0. Denis Stracqualursi and Victor Anichebe started up front for Everton with Jelavic, Drenthe and Osman only coming on in the second half with the visitors already 2-0 down.
Everton face Sunderland in the quarter-finals of the FA Cup on Saturday, but many questioned Moyes's decision to rest so many stars for a match in which a win would have seen his team go above the Reds in the table.
Moyes was coy when asked if a busy schedule had made him make six changes from the side which beat Spurs for the short trip across Stanley Park.
"We've got a big week," Moyes said.
The defeat also left Moyes, who celebrates the 10th anniversary of his appointment this week, without a win at the ground. Yet he said the result was no more deflating than any other defeat.
He said: "I am hurt because I am the Everton manager and I have lost to my rivals, Liverpool. I am the same all the time. We will get on with the next game.
"It doesn't make any difference. It is not about me, it is about the Everton players."