Anichebe was preferred to Nikica Jelavic for the second successive match and responded with a goal in the Toffees' last-gasp 3-3 draw at home to struggling Aston Villa.
"I wouldn't look too far into him not playing," Anichebe said. "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 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."