“It did not look clear and obvious to me,” said ex-Liverpool boss Rodgers.
Leicester midfielder James Maddison had earlier cancelled out Mane’s opener when he made it 1-1 in the 80th minute.
“We are bitterly disappointed to concede the penalty,” added Rodgers, making his first return to Anfield since 2015.
“I think Sadio Mane made the most of the contact. I don’t think if it had not been given by the referee it would have been overturned by VAR. When the referee gives decisions it is hard for them to overrule it.”
Maddison, who scored with Leicester’s only shot on target, said the penalty was “very soft”, adding: “I don’t think the contact warrants the way Sadio Mane went down.”
However, Liverpool manager jurgen klopp insisted the foul was “obviously a penalty”.
Liverpool have not dropped points in the premier league since March. The last time they did so at Anfield was against Leicester in January, and the Foxes were just moments away from repeating that feat here.
Klopp’s side are now on a 17-game winning streak and lead manchester city by eight points.
“Without luck we cannot win the amount of games we have won, but over the 90 minutes we deserved it, we deserved the three points,” added Klopp.
‘How can he be OK?’
Klopp, who replaced Rodgers as Liverpool manager in October 2015, said Leicester midfielder Hamza Choudhury’s tackle on Mo Salah late on was “dangerous as hell”.
Choudhury received a yellow card while Salah had treatment on the pitch and was seen limping through the media zone after the match.
“How can he do it? The ball is far away. He has to calm down. This is not the first situation. Super player, but these kind of challenges? No,” said Klopp.
“I don’t need to be a football manager to know this kind of challenge can cause a serious injury. I just need two eyes.”
Asked if Salah had picked up an injury, Klopp told Sky Sports: “How can Mo be OK? How did he [Choudhury] only get a yellow card? Mo limped off the pitch. It was done to slow Mo down and that is not OK.”
Rodgers said Choudhury was an “honest boy”, adding: “I don’t think there was anything malicious in it.”