The 2-0 defeat by Hearts at Tynecastle on Sunday left the Hoops 10 points adrift of the champions and one behind second-placed Motherwell, albeit the Parkhead men have a game in hand on both.
Second-half goals from Rudi Skacel and Ryan Stevenson sunk the visitors, who had midfielder Kris Commons sent off by referee Craig Thomson in the 65th minute for a reckless challenge on Adrian Mrowiec.
The Celtic right-back admits the tenacity which has underpinned the Light Blues' squad in recent seasons is missing at the other side of the city and accepts that they have to find it before it is too late.
"I think that is the aspect we have to improve on," said the Wales international.
"We have great footballers in the team but when we are not playing well we need to do the other side of the game better.
"They (Rangers) can play that way but we have to learn and learn quickly because if the gap gets any bigger we will have no chance. We can't afford to lose another game.
"We know we have good players here, we will gel eventually but we are not happy with the start we have made.
"I think we now have to put a decent run together and not lose again because if the gap gets any bigger it will make the challenge even harder."
David Templeton, who was involved in both Gorgie goals, revealed a pre-match pep talk from Hearts owner Vladimir Romanov spurred the players on.
"He came in to the meeting room before kick-off," said the Jambos' wide man.
"He had a few words and told us to go out and have a good performance and be on our toes because Celtic played well against us last time.
"I think it worked."
Templeton insists Celtic deserved to finish the game with 10 men, a view shared by Hoops manager Neil Lennon who criticised Commons for letting the team down.
"I had a good view and I think it was a bad tackle," said the Hearts player.
"He had a couple of little nibbles from other players when he had the ball and when he lost it he just lunged in.
"So I thought the referee got it right."