The Uruguayan striker thought he had won the game after finishing from close range after Sebastian Coates rose above Phil Jagielka, but the goal was chalked off and the sides shared the points.
And while Rodgers was disappointed with the decision from Andre Marriner's officiating team, he spoke of his delight at the performance of his side, particularly his forwards Suarez and Raheem Sterling.
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"[Suarez] was outstanding, he's so clever and bright. In the second half we put Sterling up with him and I thought [Sterling] was brilliant as well carrying the can, twisting and turning.
"Luis gets a wee bit of stick but his performance level on the field and every day in training means he is a joy to work with. When he plays with the quality that he did today he deserved a hat-trick and only the officials denied him that."
Rodgers revealed he was pleased his side were able to adapt to cope with Everton's aerial onslaught in the second half, and praised the courage his side showed to prevent the Toffees from going on to win the game.
"It was a wonderful game, I'm very very proud of the team today," he added. "Everton are a strong side who've started very well. We're still getting together and finding out how we play.
"We had to make a tactical change at half time due to a lot of direct balls. There no great build-up play [from Everton], we had to deal with a lot of aerial balls in the box.
"I'm very proud of the team, the young players were fantastic, showing great courage and right the way throughout the team it was a good point for us."
And the Liverpool manager suggested the speed with which his team went two goals up may have actually played a part in his side's downfall.
"Two-nil is always a difficult scoreline especially so early on, and it's a difficult place to come and get a point," he concluded.