Anichebe's brace against Hull City helped Sunderland to a 3-0 win and Moyes thinks the striker is now settled at the club.
Anichebe and Moyes who have together before at Everton reunited at Sunderland over the summer.
After struggling to settle at the club, Anichebe on Saturday scored in consecutive games for only the second time in his Premier League career.
His brace against Hull City helped Sunderland to a 3-0 win and Moyes thinks the striker is enjoying love from the fans.
"I think he (Anichebe) needs a lot of love. I think he wants to be respected. He's probably been to a lot of places where he's may be not had that," the Black Cats manager told Northernecho.co.uk.
"I've always respected him and he knows that I think that's why he came to play here. It makes it a lot easier for him.
"He is that sort of boy and I think at the moment the crowd are enjoying him.
"When he's on top of it, he can be just like he is now. He was never quite there in the past, but I think he's had confidence because I think the players like him and he's settled in really well."
Anichebe will hope to continue with his goal scoring form when Sunderland travel to Anfield to face Liverpool on Saturday, November 26.