Celtic had dropped points just once in the Scottish Premiership prior to the match and were on course to maintain that record thanks to Stuart Armstrong's goal in the 35th minute.
But Rangers, who had new boss Pedro Caixinha watching on from the stands, earned a point when veteran Clint Hill equalised with just three minutes remaining.
Rodgers' side still lead the way at the top by 25 points and the Celtic boss is happy their unbeaten league run – which now stands at 29 matches – remains intact, even if the failure to see out the win will take a few days to accept.
"It felt like a defeat a little bit, especially conceding in the 87th minute," Rodgers said in quotes reported by BBC Sport. "But I'm proud of the team, they battled really hard.
"On a difficult pitch I felt we weren't as fluent as usual in the first half. We were passing backwards and sideways instead of forwards.
"We made a change at half-time and I thought we had much better control in the second half and we looked like we were going to go on and score more goals. It was disappointing we conceded a goal.
"When you concede late on it feels like a loss, but, in the next couple of days, we will realise we have kept our run going and we are still unbeaten."
Rangers goalscorer Hill was delighted that his side proved their critics wrong by matching the runaway league leaders over 90 minutes.
"It was a great point by the lads, we never stopped from the first minute until the last," he told Sky Sports. "We showed spirit.
"We've been questioned by various pundits, speaking absolute nonsense all week, about our character, how we're going to be weak and all this garbage.
"I think we proved a few people wrong there. It's a great point and I'm happy for the fans - they've been through the mire in the last few years."
Hill added that Rangers were determined to impress in front of Caixinha.
"Obviously he's come in overnight, so hopefully he'll take a lot of positives out of that as well," Hill added. "We're all on show again and everyone's got to stand up and deliver."