Suárez had fired the Reds into a 2-0 first half lead after his cross was inadvertently turned into the net by Leighton Baines, before the Uruguayan glanced Steven Gerrard’s free-kick past Tim Howard.
But David Moyes’ men fought back to level through goals from Leon Osman and Steven Naismith, and Suárez then had what looked to be a legitimate goal ruled out for offside in stoppage time.
“Obviously I’m bitterly disappointed [with the last minute disallowed goal] because it was a brilliant game and I thought we stepped up well in the second half,” said Rodgers, whose side are 12th in the table.
“I was so disappointed that it didn’t count because for me it was an easy decision. The ball has come from deep and it is in the air for quite a long time. The official is just looking along the line and Coates is clearly onside when he heads it.
“It’s a wonderful finish [from Suárez] and he should have had his second goal of the game.
“It would have been a well-deserved and brilliant win for us. Instead, we are frustrated but at the same time I am very proud.
“I look at my team here today in a real cauldron of an atmosphere and how they stood up to everything against a very, very experienced team.”
Moyes, meanwhile, praised his side’s character after they fought back to deny their fierce rivals a win at Goodison Park.
“It was a good game, really exciting,” he said.
“It was a disappointing start but our boys showed great character to come back and I thought we were a bit unfortunate to not to go in 3-2 up at half-time.
“It was a really good game, end to end, and either team could have won it.”
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