It looked like the Premiership leaders would take all three points at Easter Road when Scott Sinclair grabbed two goals in four minutes after the break.
However, the home side fought back and former Celtic defender Efe Ambrose reduced the deficit before substitute Oli Shaw levelled three minutes later.
Parkhead defender Mikael Lustig then cleared a shot from Shaw off the line in a thrilling last few minutes when both sides could have won the game.
Celtic boss Rodgers said: “To lose the game would have been a crime. We were 2-0 up going into the last 15-16 minutes of the game and we should have been probably four or five up.
“Everything from our defensive pressure in the game, they didn’t really have anything against us.
“There was one chance in the first half where Martin Boyle got down the right and got a shot, but apart from that we had great comfort in the game.
“At 2-0 up with 15 minutes to go it looked as though we could go on and get more goals.
“But 2-0 in football is the most dangerous scoreline you can have, because at 2-1 – from them being not in the game really – they have that momentum and they can be free and there is no pressure, they can just play.
“I was really happy with a lot of the game, how we played, our composure, as it’s a tough place to play.
“They are a tough team. I thought we were much the better team without getting the result.”
Asked about the contest between Celtic skipper Scott Brown and fellow Scotland midfielder John McGinn, which provided an enthralling sub-plot, Rodgers backed his own player to the hilt.
“There is no contest,” he said. “Scott Brown was the exceptional midfield player on the pitch.
“John McGinn is a good player, good drive, good energy but Scott Brown is the exceptional midfield player in Scotland and he has shown that, not just in Scotland but in the Champions League.
“So he (McGinn) will have a way to go before he would be at that level.”
Hibs manager Neil Lennon was at odds with his fellow Northern Irishman’s assessment.
“I totally disagree with that,” said Lennon, who admitted it would have been fortunate had Hibs snatched the win.
“McGinn was superb, physically, his football was good.
“I don’t remember Broony dominating the game and in the last 20 minutes John got stronger when we put him back in his natural position. He was magnificent.
“Maybe Brendan sees it differently from me. I thought McGinn was a cut above.”