Celtic could not even do what they had to do - beat Hearts - as Rangers wrested the Scottish title from their grasp with little last-day fuss.
Hearts goalkeeper Marian Kello denied Celtic with a series of first-half saves, while Scott McDonald squandered a glorious chance in front of goal.
Celtic defender Gary Caldwell cleared a Calum Elliot shot off the line.
Kello was Hearts' hero again after the break as Celtic failed to claim their fourth championship in a row.
Celtic had gone into the game knowing that the destiny of the Scottish Premier League crown was not solely in their own hands, needing to win and hope that Rangers failed to win away to Dundee United to leapfrog their city rivals.
Yet home manager Gordon Strachan was an oasis of calm during his pre-match radio interview in a Celtic Park that was a sea of nerves.
Strachan made a tactical switch by fielding Darren O'Dea in place of Lee Naylor at left-back.
It meant that the Irishman was up against another surprise choice, young David Templeton being played wide on the right in place of Bruno Aguiar, who is poised to leave Tynecastle in the summer.
Marius Zaliukas was back from suspension, taking the place of the injured Ruben Palazeulos, and the Lithuanian's strength was needed in the early stages as Celtic pushed for an early goal.
Celtic fans knew the title was going to Rangers long before the final whistle
There was little initial reward for the home side other than a long-range free-kick from Shunsuke Nakamura as Hearts settled.
But Celtic squandered a great chance when a Scott Brown drive from the edge of the box was parried by goalkeeper Kello and McDonald wildly sliced his attempt to finish from 10 yards.
Hearts, who at times looked like a side whose season had finished with the clinching of third place last weekend, were being pushed back now and Kello did well to turn a low drive from Aiden McGeady on to the post and wide for a corner.
Nakamura was next to test the goalkeeper and there were no takers as Kello parried the ball across his own goalmouth.
Celtic's Japanese midfielder then just failed with an attempted lob over the goalkeeper from the halfway line.
Hearts had rarely been seen as an attacking force until the stroke of half-time, when a shot on the turn by Elliot went through goalkeeper Artur Boruc's legs but was cleared off the line by Caldwell.
That coincided with news that Rangers had gone two goals ahead at Tannadice and the SPL helicopter turned towards Tayside.
Jan Vennegoor of Hesselink replaced the ineffectual Georgios Samaras at half-time, but it remained flat at Celtic Park until the Hearts fans found their voice with the news that Rangers had scored yet again.
McGeady fired wide from 14 yards and Eggert Jonsson produced a fine last-ditch challenge to deny McDonald.
The Australian striker was replaced with Shaun Maloney, an indication that Strachan had already conceded the title, although Kello was forced into a couple more saves, denying Scott Brown and Nakamura from the resulting corner.
Brown was himself replaced with Willo Flood as Celtic ended the season with one win in their last four games and relinquished their title with a whimper instead of the expected bang on Helicopter Sunday.
Celtic manager Gordon Strachan:
"Today, it wasn't good enough. The game was dead after the result filtered through.
"But, at this moment in time, we'd like to thank the players and staff. They gave it their best shot.
"I'd like to thank supporters. It wasn't easy for them today.
"We weren't up for the challenge of winning four in a row."
Hearts manager Csaba Laszlo:
"If you get a draw here at Celtic Park it's a good result. At the end of the season it was important to play successful football, like we did before.
"Everybody is satisfied with this result.
"I wish all the best for Celtic in their Champions League qualification games and I hope next season we can have successful football with Hearts and that in the Europa League we can have good performances.
"We must look for new players. We must try to plan and find players with the will and the character to play for this club. If we are focused, I think we can get some good players."
Celtic: Boruc, Hinkel, Caldwell, Loovens, O'Dea, Nakamura, Scott Brown (Flood 82), Hartley, McGeady, McDonald (Maloney 69), Samaras (Vennegoor of Hesselink 46). Subs Not Used: Mark Brown, Crosas, Conroy, Naylor.
Hearts: Kello, Neilson, Karipidis, Mrowiec, Lee Wallace, Jonsson, Michael Stewart, Zaliukas (Johnny Stewart 80), Obua, Elliot (Nade 61), Templeton (Novikovas 51). Subs Not Used: Balogh, Tullberg, Thomson, Park.
Ref: C Thomson
BBC Sport Player Rater man of the match: Hearts' Marian Kello 8.50 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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