Steven Gerrard broke the deadlock in the Merseysid derby in the 65th minute with a powerful free-kick which beat Everton goalkeeper Tim Howard.
Mario Balotelli, who moved to Liverpool from AC Milan in a £16m deal this summer, was denied by Howard’s shoulder and the woodwork in the second half.
And Liverpool were made to pay for wasting chances to extend their lead when Everton skipper Jagielka finished past Simon Mignolet from the edge of the area.
“The players were brilliant. We were clearly the dominant side in the game, but sometimes you don’t get what you deserve in football,” Rodgers told BBC Sport.
“But for a wonder strike at the end of the game we would have got the three points.”
Here is a selection of the best photos from Anfield.
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