The Argentine, who has struggled with injuries in recent seasons, won a start in the 2-1 victory.
Moyes was happy with his display, but warned the playmaker that he is no longer the same player he once was.
"I thought Lanzini was very good, I don't know if he gave the ball away tonight. He has been a little bit unlucky not to play because I have seen lots of good things from him, he has had a couple of injuries which has seen him falter a little bit and maybe not sure if he was fully fit," Moyes said.
"He is another one who has played 90 minutes tonight, passed the ball well and helped us play better, he kept it [well], so I am really pleased with Manu because he is someone who I really like and he has done well previously."
Moyes added: "He has changed as a player and he has to realise that himself, he is not the same as he was probably since his since injury two or three years ago."