A 1-1 draw with Kilmarnock at Parkhead on Tuesday saw Celtic blow the chance to top the Scottish Premier League.
It was the Hoops' third successive draw in the league at home and means rivals Rangers top the league at Christmas by two points despite their game against Dundee United being postponed due to the weather.
"That was as well as we had played for a while. We should have been out of sight at half-time," said Celtic coach Neil Lennon. "We got done on a poor goal from our point of view but the least we deserved was a point tonight."
Killie hadn't won at Celtic Park in 55 years but Connor Sammon gave them hope when he fired them into a 54th minute lead completely against the run of play. The Ayrshire side desperately hung on to their lead until the 86th minute when Rogne headed Ki Sung-Yeung's free-kick home to grab a point as Celtic were left ruing a host of missed opportunities in both halves.
Kilmarnock named an unchanged side from the one which defeated Hibernian on Saturday while Celtic welcomed back Emilio Izaguirre and James Forrest for their first game in 24 days, played in subzero conditions in a sparsely populated Parkhead. After their long enforced break the Celtic players were raring to get going and put Kilmarnock under pressure from the start when Niall McGinn's shot was held by Cammy Bell.
The Hoops had the ball in the net in the eighth minute when Gary Hooper converted from Joe Ledley's lofted pass but it was ruled out for offside. Celtic cranked up the pressure but their stars conspired to miss a host of chances to open the scoring. A Hooper pass sent McGinn clear but he fired his shot off Bell's legs before Izaguirre took advantage of a loose pass on a slippery pitch to rifle in a fierce shot that stung the palms of the keeper. Daniel Majstorovic was inches away with a header before South Korean Ki curled a free-kick just over the bar.
The home side were dealt a blow ten minutes before the break when top scorer Hooper was stretchered off to be replaced by Anthony Stokes. There was still time for the substitute to fire into the side netting as Killie somehow made it to the break on level terms. Celtic were left to rue their missed chances just eight minutes into the second-half when Sammon gave Kilmarnock the lead with his seventh goal in eight games. The Irishman latched on to Mehdi Taouil's through ball and shrugged off Izaguirre's challenge before slotting low past Fraser Forster for his 12th goal of the season.
Celtic looked shell-shocked to find themselves behind and brought on Scott Brown and Paddy McCourt for the ineffective Ledley and McGinn. Sammon was proving a handful for the Celtic defence and used his strength to brush off Majstorovic in the box but could only poke his effort straight to Forster. Stokes cracked a shot over from just outside the box before Daryl Murphy missed Celtic's best chance of the half. Cha's cross was dropped by Bell and fell to the Irishman but he sent his shot on the turn over the bar.
Celtic's pressure paid off with five minutes to go when Rogne headed them level. Ki swung a free-kick from the left into the box and the Norwegian leaped highest to send an angled header off the post on its way in. Sammon came close to snatching a late winner for Killie when he rounded Forster but Majstorovic slid to block his shot.