The 19-year-old managed his first start on Saturday against Brentford, impressing the home crowd.
While Chermiti has only been involved off the bench in the past, he believes that he is set for a great next season.
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I can't explain this feeling right now," a delighted Chermiti told evertonfc.com post-game.
It was a great performance from everyone, and we did our job. Everyone is happy today. We did our job so now we can enjoy it.
It's a great feeling for me. It was a tough season because I didn't play much, but I did well today.
The most important thing was the win. As I say, I haven't played much, but 90 minutes today was a good feeling."