The Reds and Toffees drew 0-0 at Anfield but visiting boss David Moyes was left to regret a decision made when defender Sylvain Distin headed home in the second half but whistleblower Oliver pulled up Victor Anichebe for a foul on goalkeeper Pepe Reina.
Moyes rued the decision but Rodgers, understandably, believes it was the correct call made by the match official who in his eyes had a very good game.
"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 per cent 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 today."