The 220th Merseyside derby ended goalless but the Toffees boss was unhappy Sylvain Distin's second-half header was ruled out for a foul on goalkeeper Jose Reina.
A draw extended Everton's winless run in the league at their near-neighbours to 14 years - beyond Moyes' time at the club - but the Scot said that had his side got their fair share of decisions in that time, their results would have been dramatically different.
"It was a legitimate goal. The goalkeeper runs into Victor Anichebe and it is a goal," he said. "The referee said Victor impeded the goalkeeper but the goalkeeper ran into him so it can't possibly be a free-kick. It is not a foul. It is disappointing because it is not easy here.
"You people (the media) are quick to remind me I've not won at Anfield but if you don't get any decisions at Anfield it makes it very difficult to win and that (not getting decisions) is quite a regular occurrence when you come here."
However, opposite number Rodgers insisted referee Michael Oliver was right in his assessment.
"I think when you see it again the referee has good sight of it early," he said. "As the ball has virtually left the corner he has blown up for a foul.
"I wasn't 100% sure at the time it wasn't for Distin's foul on (Jamie) Carragher or whether it was Anichebe but I think it was Anichebe's initial push.
"It is one of those where if you are the manager you probably see the decision as the correct one.
"I am sure David will be disappointed the goal did not stand but I thought Michael was very good."
- Sports & Recreation
- Sylvain Distin
- Victor Anichebe