Liverpool and Everton ended scoreless at Anfield which leaves Everton on the verge of a sixth place finish.
Marouane Fellaini and Daniel Sturridge had the best chances for their respective teams.
The Toffees thought they had taken the lead in the second half when Sylvain Distin headed in a corner. But it was ruled out for a push on Jamie Carragher who was taking part in his 30th and last Merseyside derby.
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Everton are five points clear of Liverpool with two games to go.