Barkley's all-round performance won all the plaudits afterwards, and Howard is confident the England Under-21s international can flourish under the new Toffees boss.
He told the Liverpool Echo: "He believes in himself. He's got real mental strength. He's an exciting prospect and now it seems he's on the cusp of trying to fulfil that potential rather than just being a name who is talked about.
"He has a lot ahead of him and he's only a young man, but he has a good mentality and we'll keep pushing him.
"We know he can shoot with both feet so the goal wasn't a surprise to us, we've seen him do it every day in training."
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