Anichebe scored his eighth goal of the season, and his sixth in 13 Premier League starts, in the Toffees' 2-0 win over QPR on Saturday.
And with Nikica Jelavic having netted just one league goal since 8 December, the 24-year-old's form has helped Moyes' side maintain their pursuit of a UEFA Champions League place.
"He has been terrific," said Moyes. "The boy has an awful lot going for him and I've said many times he's just needed to have a bit more self-confidence.
"I think he has a bit more to do but we have got signs of someone who could be an outstanding player.
"It has taken a while for him to show us that but how he has been playing is very good and is playing as well as anyone - but we needed it because we've been a bit short there.
"We just want him to keep playing the way he is doing; he is helping us at the moment and gives us an alternative.
"I think for Everton we need people who are getting in double figures (for goalscoring). We've really missed someone getting in the high teens with their goals.
"I hope he gets some more because it will help us until the end of the season."
Everton are currently sixth in the Premier League table, three points behind Chelsea and Tottenham, in fourth and fifth respectively, but having played a game more than the former.
On Tuesday, the Toffees travel to the Emirates to face Arsenal, who are four points ahead of them in third place.