The win marked Barry's 500th appearance in the Premier League.
"It's fantastic," Barry told Sky Sports 1. "I'm really lucky to be able to achieve 500 games. I've stayed injury free, touch wood, this long and I want to keep going and help Everton up this league table.
Romelu Lukaku says he has been waiting for his Goodison Park debut for a long time after Everton's 3-2 win over Newcastle.
"Fifteen years ago I was making my debut. Time flies, especially when you're playing Premier League football, which is what you dream of as a child, so I want to try and play as long as possible."
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