Anichebe was the preferred forward for the second successive match and responded with a goal in Everton's 3-3 draw at home to Aston Villa on Saturday.
The goal marked the Nigerian's fifth in eight league starts, with Jelavic scoring his last top-flight goal almost two months ago.
Anichebe said: "I wouldn't look too far into him not playing.
"Nikica has been unbelievable since he came to us and his record speaks for itself (18 goals in 45 appearances).
"I was injured for two months and he took the burden on his own and he has been playing on his own every game.
"There comes a time when you have to take him out, because he is pretty tired but the best of him will come.
"He has been playing for a long time on his own. Now I am back it is probably a good time to give him a rest.
"I talk to him all the time and some of the positions I am getting into is because of him, he has helped me get into more goalscoring positions.
"We can play together. If he doesn't play, if I don't play, it is not a big deal."