Anichebe nodded home the 64th-minute equaliser on his first appearance for two months in his injury-hit season. It was also the first headed goal West Ham have conceded this season.
"Anichebe's a really good player, he just needs to believe in himself a little but more because he's got something about him," Moyes said.
"He continues missing chunks of it which stops us using him.
He'll play a big part, he's a really important player, he can do two or three jobs for me and he took his goal well."