Harry Redknapp's makeshift squad battled relentlessly against the Ukrainian champions only to concede two goals late in the game.
Second-half substitute Yevgen Seleznov scored within seconds of coming onto the pitch with a leaping header past Heurelho Gomes.
Jadson added to Spurs' woe when finishing off some terrific link-up play with Willian just minutes later.
Busy ScheduleWith six games in 17 days, including the Carling Cup final against Manchester United, Redknapp had feared losing players to injury on a surface he branded unfit for non-league football.
It meant Redknapp wanted to rest the likes of Luka Modric, Jonathan Woodgate, Wilson Palacios and Aaron Lennon - he had an entire team back in London taking injuries and ineligibility into account.
Dean Parrett, 17, made an encouraging debut and only Michael Dawson and Jermaine Jenas remained from the side that drew with Arsenal in their previous game.
While Spurs' problem is fixture congestion, Shakhtar have been on a winter break and had not played in more than two months - but they showed no signs of being rusty when play got started and could have wrapped up the tie with sharper finishing.
Mircea Lucescu's men are still upset over a controversial defeat by Barcelona - they felt the Spanish giants should have sportingly given the ball back for one of their goals - that effectively knocked them out of the Champions League.
They played like they wanted to settle a score. Two of the four Brazilians in their starting XI combined for an effort in the fifth minute, with Ilsinho wriggling into the penalty area and Jadson firing wide of the post.
Shakhtar also had a penalty shout turned down, then Darijo Srna had a free-kick blocked after Fernandinho went over theatrically following a challenge from Jenas.
Razvan Rat volleyed over the crossbar after drifting to the far post as Shakhtar applied their early pressure.
Dawson was needed to bravely block a shot from Mariusz Lewandowski and Gomes could not get his hands on a Srna cross - but there was no Shakhtar player to apply the finish.
Defensive tacticsIt was backs-to-the-wall defending from the visitors and Dawson was holding it together for them.
He made a last-ditch tackle to deny Olexandr Gladkiy, and moments later the striker was put through on goal but somehow volleyed his finish backwards.
It took 32 minutes for Spurs to create their first effort. Parrett played in Giovani dos Santos down the left but the Mexican's shot, on his first start under Redknapp, crashed into the side-netting.
Shakhtar continued to attack and Willian fired straight at Gomes before the break, then Fernandinho shot wide from long distance.
The hosts should have been ahead three minutes after the restart with a flowing move from right to left. Jadson shifted the ball to Ilsinho, then Willian drove his shot across the face of the goal and Pascal Chimbonda, making his first start since rejoining Spurs from Sunderland, cleared for a corner.
Spurs almost hit Shakhtar on the break when Giovani played a ball over the top for Jenas. Redknapp's skipper on the night poked the ball past goalkeeper Andriy Pyatov but there were no team-mates around to finish off the move.
GoalShakhtar's first goal came with 11 minutes remaining, with substitute Seleznov glancing home a Jadson free-kick.
Seleznov beat the punch of Gomes, who then needed treatment for a knock.
Jadson added the second two minutes from time, wriggling into the penalty area and finishing low into Gomes' bottom corner.
1st Half Goals
Shots on Target
Shots off Target