Anichebe made his return to the Everton side on New Years Day against West Brom after a four-month groin injury by scoring the only goal in the Toffees' 1-0 win.
Moyes was delighted with the 23-year-old's contributions but believes that Anichebe can achieve more - only if he wants to.
He said on the Mirror: "Victor has all the attributes to be a really good player. He needs to want it himself,
"If we can get him on the pitch, he is a good boy. He just needs a shake to keep him alive at times. But he has got attributes and we have played him in some big games.
"He does lack belief and needs support. I hope he gets the support from me and the staff here. I think we do give it to him."
Anichebe has only made 94 appearances in his five-year stint at Everton due to a series of injuries.
He missed out on 11 months of football after suffering a shin break in 2009 and missed the start of this season after sustaining a groin injury while on international duty with Nigeria.