"He always was a really good football player, but once he got used to the physical elements of the Premier League he developed into a really good captain, he was always a really good professional," said Moyes.
"His professionalism rubbed off on a lot of people at the time, and I was really fortunate to have people like Mikel and others around me who were really good players."
Moyes singled out Arteta as a pivotal part of his old Everton team.
He said: "Mikel gave us something different. Probably the biggest disappointment was when I had to sell him to Arsenal.
"At the time he wanted to go, Arsenal was a good move for him probably at the right time in his career but I have to say we missed him because he was an exceptional player."