Cleverley has been on the sidelines since August 29after injuring his ankle ligaments during the clash against Tottenham Hotspur.
Cleverley said: "There's nothing like playing football in competitive matches, so it was nice to be back. I've obviously not had much chance to play at Goodison, so that made it an even better exercise for me and I'm just a bit disappointed with the result (Everton lost 1-0).
"But I came through okay, I felt quite sharp, especially in the first half, and for me, personally, it was a good hour under my belt and a big step in my rehab. It was always the plan to get 45 minutes to an hour, so I'm pleased to come through it.
"I'll see what the manager thinks, see how he feels I did tonight and hopefully I wake up in the morning, everything's fine and I'm available for Saturday if he wants to use me."