Writing in his match programme notes, Coleman said: "I would like to offer a special personal welcome to David Moyes on his return to Goodison. He did a fantastic job for our football club and I will forever be grateful for the opportunity he gave me and the way he looked after me and my family.
"The win against Sheffield United on Boxing Day was great for us. It wasn't a classic game by any means but sometimes it's just all about the three points. No team will perform well in every game and when that happens it's important to make sure you at least take something from it.
"We stuck at it and I thought we thoroughly deserved the victory.
"I am writing these notes on the morning after what should have been the Manchester City game and to see us lying third in the Premier League table is so satisfying. The league is very congested with very few points separating teams in the top eight or nine positions and it's all about staying in or around those places."