Celtic goalkeeper Scott Bain is confident the champions can go on the sort of winning run that has carried them home in recent seasons.
Hibs had led 2-0 with 11 minutes left before Odsonne Edouard's penalty and Diego Laxalt's stoppage-time leveller prevented Celtic from slumping to a fourth defeat in eight games.
Celtic had won eight on the spin before this difficult run and put together 12 and nine-match winning streaks in all competitions before and after last New Year.
And Bain is sure they can rediscover their consistency.
"We have always shown it before," he said. "You have seen at the turn of the year the last three or four years, how we have really steamrollered teams from then on.
"There's a lot of games to be played, December is a really busy month, so we need the full squad to be together for that.
"Until you get to December, you want to be there or thereabouts, but you know in the months towards the end of the season when it really matters, you have seen this squad really pushes on and goes from strength to strength.
"Obviously we want to get that quicker in these couple of months but there's a lot of games to be played."
The right-back then allowed the goalscorer a free header to set up Kevin Nisbet to evade Bitton and fire home.
Bain added: "We seem to be making mistakes and being punished for it, that's the way it is going right now. But it's a case of digging ourselves out of it and pushing on.
"I don't think we are too far off. We probably should have been way ahead before they scored."
Lennon denied their title hopes were hanging by a thread but warned his players an improvement in attitude was needed.
"There is a long way to go," the Celtic boss said. "But what I'm looking for is a level of performance, getting a run together. But the attitude of some of the players has to be better.
"The game was endemic of our season: we had a good spell, a really poor spell and then 20 minutes of brilliance. So they are capable of that, but they have got to start really wanting to put it all together for the 90 (minutes).
"The players have to start concentrating and show a lot more desire than what they are showing.
"This team is capable of going on a good run but they have to be all together, they have to be mentally tuned, week in, week out. It was apparent that some of them switched off mentally.
"We don't do the dirty bits of the game well enough at times and we need to get rid of that softness, because teams are highly motivated to play against us."
Murphy felt Hibernian's performance was an important statement after defeat by Aberdeen followed their Scottish Cup loss against Hearts.
"Obviously it was a big disappointment, and the game against Aberdeen was as well," Murphy said.
"So this was a big game for us and we managed to put in a performance. We should have probably won the game in the end but the boys left everything out there."