Moyes challenged the former Sligo man to build on his breakthrough season and continue his development next term.
"In the first six or seven months of last season he gave us great impetus, he was the one we were looking to in spells," he told evertonfc.com.
"That fresh, real honest, just glad to be on the pitch approach was something I think the supporters recognised and appreciated. I think in the last few months he went off a little bit, I think after the last time he came back from international duty he did not come back firing like he was before.
"As I have said, sometimes there are things about Seamus when you can see why he was a £60,000 player and then there are other times you will look at him and say that is great business.
"Overall, his progress for us - from his loan move to Blackpool to coming back to us - you can see the strides he has made. He really has stepped up massive levels in a short space of time and we are hoping for him to keep that going over the coming seasons."