The England international impressed during victory over Chelsea.
Barry said: "Nobody is that stable and nobody looks like they will run away with the league. That means there could be a surprise this season, you never know.
"And from an Everton point of view we want to get into the mix and finish as high as we can. Getting into Europe with Everton has to be a target. And the longer the season goes on the more we'll set ourselves more targets."
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