Anichebe suffered a groin injury when on international duty with Nigeria in September and then an ankle setback with the Toffees.
But he marked his return by coming off the substitutes’ bench to net an 87th-minute decider against Roy Hodgson’s side.
Everton manager Moyes said: “It was a serious injury. Victor has had no games. I’ve not even had him playing in reserve games. Then he had an ankle injury when he came back in training.
“He is someone we have missed because we can play him in several roles and he is someone who has got a lot of potential if we get the opportunity to unwrap it. He is a good all-round forward player; he can play wide, he can play through the middle and has a lot of real good attributes which are important in the Premier League.
“He has missed a lot of football. At times he lacks a bit of self-confidence but the goal and the reaction of the supporters will help him.”
Moyes admitted he would have been content with a point from a game of few chances before Anichebe found the target.
He said: “The game overall was a draw. I didn’t think there were many chances for either of the teams.
“We tried to make it difficult for West Brom like they make it difficult for teams.
“It was a bit of a stalemate at times. I don’t think you’ll buy the DVD of the game.
“But at the end of the day, this has been a hard place for us. We’ve not won here for a while and the victory gives us a chance to look forward.
“You need to grind out results and over the years at Everton we’ve needed to do that at times.”
West Brom manager Hodgson wants to bring in new quality signings but is uncertain whether he will be given the financial backing.
Hodgson, whose current contract runs out this summer, said: “If we are going to have a good season, we need some help. Whether there are players out there who can help is another matter. I’d like to think we have got to the stage where the type of players that would help us would cost money and demand high wages. I’m not certain at the moment that is the way we are looking to go forward.
“I’m not interested in bringing bodies or extra names into the club unless I am sure they are better than what we have got.”