Matthew Shiels pulled Kirkwood’s side level after Ewen Henderson had opened the scoring but Rangers couldn’t capitalise on an improved spell after the break.
Striker Jack Aitchison hit the winner in the closing stages to ensure that the Glasgow Cup remained at Parkhead for another year.
And boss Kirkwood was frustrated that his side failed to shine under the spotlight as they slipped to an Old Firm defeat.
He said: “It is very disappointing, especially the first half hour. It is probably the worst we have played all season.
“It is a learning curve for the young lads coming to the stadium with the expectation levels, their families, the crowd. They have got to take that on the chin and bounce back from it.
“You can’t replicate those things that they have had to put up with tonight in training. You have got to learn from the hurt and try and lift themselves up.
“The first half hour, we just weren’t at the races. We got the goal and managed to get back into the game and had a couple of half chances but I think we were fortunate at half-time to be level.
“In the second half, we made a couple of positional changes and looked much more likely to get the second goal. It was a poor goal for us to concede and it was an uphill battle after that.
“We had half chances to get an equaliser and take it to penalties but overall we are disappointed.
“We have got to try and lift them up over the next couple of days and get them focused on the league now.”