Mark Clark"s side was outscored 15-0 in the final four minutes of the second period, and although they produced a spirited comeback after trailing 33-18 at half-time, the margin proved too great.
Jo Leedham led the Britain scoring with 14 points and five rebounds in the first of eight qualifying games this summer. Kim Butler added 12 points and eight rebounds for a GB side missing point guard Georgia Jones, while Megan Moody had ten points and five boards.
Clark had singled out Olexandra Gorbunova as the Ukrainian player to stop, but the small forward was able to lead her team with 18 points as they recorded the victory.
Floor shooting proved to be Britain"s Achilles heel as the home side proved more successful from both two point and three point range.
An even start to the game saw Britain"s first three points scored by Sarah McKay as they led 3-2 with 5:45 on the clock, and a Leeham free-throw followed by a Moody lay-up put them 6-2 ahead.
However, that was as good as it got in the first period, and ten unanswered Ukraine points sent the home team into the first break with a 12-6 lead.
Olena Ogorodnikova extended that lead by two with the opening score of the second period, and although Moody broke the run, the hosts led 18-8 with two and a half minutes gone.
Rose Mason sunk a single free-throw, and that launched a 10-0 British run which saw them level the score, thanks to a pair of Butler jumps shots and a Moody basket, before a Mason "and-one"€ tied things up with 4:02 on the clock.
That proved to be last time that GB troubled the scorers in the first half as the home side reeled off 15 straight points to take control of the game.
Coach Clark managed to steady the team at half-time, with Mason ending the run as she drained two free-throws to open the second half.
There was little to choose between the sides in the third period, with Butler leading the GB scoring with a three and a pair of free throws before a Leedham lay-up cut Ukraine"s lead to 52-39 going into the final stanza.
The fourth period proved to be Britain"s best spell of the game as they dominated proceedings "€Â" with Butler scoring four points in the first minute to cut the margin to nine.
Iryna Biryuk put the brakes on the comeback with a three, only for Lisa Hutchinson to reply from downtown. A pair of Leedham foul shots saw the margin cut to 57-50 going into the final two and a half minutes, and the same player laid the ball up to help Britain move within five with two minutes left remaining.
However, Leedham missed a jumper and Nikki Luckhurst was off target from three-point range before Mason made a pair of free throws to cut the lead to four at 58-54 with eight seconds remaining.
That was as close as GB came, however, as Inna Yegorova split a pair from the charity stripe to end the game.
Meanwhile six of the men"s squad made their debuts in Britain"s first test game of the summer. The British side opened the four-team tournament in Cagliari, Italy, by beating Belgium 80-64.
Britain were without Luol Deng, who is still waiting for his insurance to come through. However, Pops Mensah-Bonsu, Flinder Boyd, Nick George, Steve Leven, Jarret Hart and Kieron Achara all impressed on their first outing for GB.
Mensah-Bonsu"s determination was apparent when he went crashing into the toblerones after missing a dunk, but he had his teammates on their feet minutes later when he slammed it home. The Tottenham-born forward finished with 20 points and 14 rebounds, while George posted 10 and Achara nine.
They play Estonia on Thursday.



