(CNN) -- Tottenham face an uphill battle to qualify for the last 16 of the UEFA Cup after a makeshift side conceded two late goals in sub-zero temperatures in Ukraine to lose 2-0 to Shakhtar Donetsk.
Donetsk midfielder Willian (left) challenges Chris Gunter for the ball as Donetsk defeated Tottenham 2-0.
Faced with a hectic fixture schedule, including the League Cup final against Manchester United a week on Sunday, Tottenham manager Harry Redknapp chose to rest a host of first-team players for their last 32 first leg clash -- and the experiment looked like working until the home side made the breakthrough in the 79th minute.
A free-kick from Brazilian Jadson was glanced home by the head of substitute Yevgen Seleznov, who beat the punch of goalkeeper Heurelho Gomes to put Donetsk ahead.
Jadson himself sealed the win with just two minutes remaining, playing a one-two before wriggling into the penalty area and finishing low into Gomes' bottom corner.
Redknapp told PA Sport: "I couldn't see them scoring and thought they had run out of ideas but we gave a silly free-kick away and were punished. That's how it goes.
"It won't be easy now -- the return game is a couple of days before a cup final at Wembley against Manchester United, which is obviously a priority for us."
Meanwhile, a late goal from substitute Martin Vingaard on his debut earned FC Copenhagen a 2-2 first leg home draw with Manchester City.
City took a 27th minute lead when goalkeeper Jesper Christiansen allowed a weak shot from defender Nedum Onuoha to squirm under his body for only his second career goal.
The home side levelled 11 minutes after the interval when Ailton Almeida headed past Shay Given from a Thomas Kristensen corner.
However, City regained the lead in the 61st minute with another goal out of nothing. A cross from Shaun Wright-Phillips went through the legs of Atiba Hutchinson and direct to Stephen Ireland, who rattled a shot into the corner of the net past a stranded Christiansen.
Copenhagen equalized again when substitutes Vingaard and Dame N'Doye -- both making their debuts -- linked up in stoppage time for the former to head home.
Elsewhere, Italian side Udinese squandered a 2-0 lead at Polish side Lech Poznan, who scored twice in the last nine minutes to earn a 2-2 draw.
Kennedy Bakircioglu scored the only goal on the hour mark to give Ajax a vital 1-0 victory at Serie A side Fiorentina, while there was a superb win for another Dutch side as FC Twente secured a shock 1-0 victory at French side Marseille.