Callum McGregor gave the sell-out home crowd hope on the southside of Glasgow with a second-half goal, but by then it was already an uphill struggle for Scotland who had fallen behind in a sleepy first half.
A sumptuous little lob from Andriy Yarmolenko beat goalkeeper Craig Gordon just after half an hour, but the Scotland number one had been busy already making a series of stops to ensure the score was just one at the interval.
Roman Yaremchuk scored a header early in the second half and though Scotland rallied in the second half the deficit was too great to overcome on an emotional evening for the visitors who now head to Cardiff and, perhaps, Qatar.
They rounded it off with a late third on the counter-attack from substitute Artem Dovbyk as Scotland’s players pressed forward seeking extra-time and an extension to the World Cup dream.
Here’s how they rated.
5. Liam Cooper - 4
Part of a back-three that could just not live with Ukraine's forward line. Replaced by Hendry on 68 minutes. 4 Photo: Ross MacDonald - SNS Group
6. Scott McTominay - 4
A regrettable performance by the Man Utd player, whose distribution was off-colour. Improved a little when moved into midfield. 4 Photo: Craig Williamson - SNS Group
7. Callum McGregor - 5
Grew into the match in the second half, scoring an albeit fortunate goal and making a key tackle to keep Scotland in the match until the end. 5 Photo: Ross Parker - SNS Group
8. John McGinn - 4
So often reliable for Scotland, he had a real off-night. Slack in possession and missed a gilt-edged header from close range. Booked for a late tackle. Not his day at all. 4 Photo: Craig Foy - SNS Group