Everton's
Villa defender Tyrone Mings headed the home side's best chance wide from Douglas Luiz's cross, when he should have at least tested Jordan Pickford in the Everton goal.
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After an uninspiring first half, Carlo Ancelotti's Everton improved after the break with Ben Godfrey drawing a save from Villa keeper Emiliano Martinez.
But Everton failed to create any clear chances late in the game and the result left the Merseyside club eighth in the table, eight points adrift of fourth-placed Chelsea.