Phil Jagielka rescued a point for Everton in some style with a powerful injury-time equaliser from long range.
The defender's stunning strike cancelled out a 65th-minute opener from Steven Gerrard, but Rodgers believed Liverpool should have been awarded a spot-kick inside the first 10 minutes when Gareth Barry appeared to handle a goal-bound shot from Raheem Sterling.
Barry was not penalised by referee Martin Atkinson, much to the frustration of the hosts' manager.
After claiming in his media conference that Liverpool should have had a penalty, Rodgers was asked to clarify which appeal he was referring to.
"The one where the ball was shot into the box and Gareth Barry grabbed it with both hands, that one," he responded.
"That was nearly a save. And I don't know what Martin was seeing because he had a good look at it.
"If your arms are above your head and you stop it as blatantly as that, how it's not a penalty I'll never know."
Barry was already on a booking at the time and Rodgers added: "Maybe that was in the referee's mind. For us it was disappointing because it was a clear handball.
"We certainly didn't get what we deserved. I think it was very clear we were much the better side, and when you concede a goal like that so late on, it probably epitomises the luck that went against us. I never felt in any danger in the game."
Rodgers could at least take heart from an improved Liverpool performance and the contribution of Gerrard, who has been criticised for his recent displays.
The former England captain looked to have sealed three points when he beat Tim Howard with a curling free-kick from 25 yards to score his ninth goal in Premier League Merseyside derbies.
"He's shown many times over the years that's his range," said Rodgers.
"He's such a selfless guy, Stevie. And he was letting Mario [Balotelli] take a few [free-kicks] in the first half and I was screaming for him to take it because he's got so much quality.
"It was a goal that should have won the game, a wonderful free-kick, and I thought his performance was outstanding.
"I'm very proud of the players. We took the lead, arguably should have had at least two more and should have definitely had a penalty. So I think for us, it [the result] was disappointing but the performance was at a much better level."
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