The former Rangers and Livingston player was one of a handful of players who had battled back from injury to take their place in the starting line-up and, along with fellow defender John Souttar, made it through the full 120 minutes.
But there was only pain at the end, after two Rangers goals in extra time from Ryan Jack and Scott Wright sent them home without the trophy for the third time in four seasons.
“It’s tough, we are really disappointed,” said Halkett. “But I think in a few hours time or a few days time, when we look back and reflect, we can all be proud of ourselves for the season we’ve had.
“Coming straight back up from the Championship, finishing third, guaranteeing the club European football and reaching the cup final – it’s disappointing not to go all the way and win it but we gave it a good go.
“We took it to extra time but Rangers just had too much on the day.”
They pushed the Europa League finalists all the way, starting the game with purpose. They were under the cosh more in the second half but were resolute in forcing extra time.
“There was clearly not much between the teams over the 90 minutes. We had a gameplan and stuck to it very well,” said Halkett, who has struggled with an ankle injury since the semi-final and, having played through the pain barrier, will now weigh up whether he needs an operation ahead of the new season.
“We had a gameplan and limited Rangers to a small number of chances. We had a couple of chances ourselves. Big Ellis [Simms] had a right good chance and he was unlucky.
“But when it went to extra-time and they got the first goal from the corner, we defended the first ball but it was a great strike from Jack at the edge of the box, it seemed to deflate us a wee bit.
“Once they got the second goal, we started to chase it a wee bit and the boys started to get a bit tired.”