The 24-year-old made his comeback after two months on the sidelines with a goal in last weekend's come-from-behind win at West Ham.
"Victor has played very well. He is an important player for us and a lot people under-estimate what he can do for us," said Moyes. "Not having him available means we have not been able to change many things in the attacking areas."
With Kevin Mirallas, arguably the Toffees' best attacking outlet this season, struggling with a hamstring injury Anichebe's return could not have been timed better.
"Not having Mirallas available for the last couple of months at different times has meant we have been limited in forward areas and probably not won as many games as we should have," Moyes added.
"We want to keep him (Anichebe) fit and him to have a bit of self-confidence and I am sure that goal will do that for him."
Everton host bottom-three side Wigan on Boxing Day without midfielder Marouane Fellaini, who serves the second of a three-match ban for headbutting Stoke's Ryan Shawcross. But Darron Gibson will be available to face Latics, despite the midfielder's red card at Upton Park as an appeal is pending.
Gibson was dismissed by referee Anthony Taylor for a challenge on Mark Noble but as the Football Association require two working days to deal with an appeal, the Republic of Ireland international has had his ban suspended until his case can be heard later this week.
"We think there's a real reason to ask the FA to re-look at it," said Moyes, who believes Wednesday's opponents have not had the credit they deserve despite being in the bottom three.
"Roberto has done a really good job there, he has a good technical side and they are a test for all teams. Folk think their league position is a guide but I don't think so, I think they have played some good football and we will have to do all the right things."
Source: PA
Source: PA