It was Ayr’s second cruel defeat to the Old Firm in the space of a week after losing 4-0 to Rangers in the CIS Insurance Cup and O’Neill admitted the scoreline also flattered Celtic.

The Celtic boss said: ‘‘We knew it would be a difficult game, but on the evening the accolades go to Ayr. They were magnificent they didn’t deserve to be beaten.

‘‘They might not have deserved to be beaten 4-0 last week, but they certainly didn’t deserve to be beaten 3-0 tonight.

‘‘When we got the goal just after half-time I thought we might settle down, but after that goal Ayr had their best period of the game.

‘‘They were unlucky not to equalise and at 1-1 it would have been a different game.

‘‘One hit the bar and Rab Douglas made a great save, but we needed great goals to win the game.’’

But while heaping lavish praise on the First Division outfit he admitted that his side could have been better - and was relieved to be in the final of the Scottish Cup.

They will now play the winners of either Rangers or Partick and O’Neill added: ‘‘It’s very easy to be patronising, but you can’t take anything away from Ayr.

‘‘Their cup exploits have been terrific and results in both competitions extraordinary.

‘‘The game last week would have given them great heart and they played very well again.

‘‘I thought that we could have been better, but I’m delighted to go through.’’

Ayr manager Gordon Dalziel was also full of praise for his team and insisted that the scoreline was unjust.

James Grady hit the bar and also saw his shot saved by Robert Douglas after Celtic had opened the scoring.

But lightning struck twice again with Thompson’s late double taking the gloss off Ayr’s brave performance.

Dalziel said: ‘‘I thought the players today were superb. We played great football and created a lot of chances.

‘‘I thought it was a wee bit cruel at the end to lose 3-0. The players didn’t deserve that.’’

Dalziel reckons his players deserved at least to score a goal at the national stadium.

He added: ‘‘I thought we bossed it in the second half and the players, the supporters and everybody involved in the club were a different class tonight.

‘‘The only disappointing factor was that over the 90 minutes against Celtic we deserved to score a goal, but it wasn’t to be.

‘‘I’m so proud of my players. We played a class side and everyone in that dressing room is delighted with the way we played.

‘‘This season has been magnificent and I couldn’t ask more from my players.

‘‘We now play Arbroath on Tuesday - that’s what they mean about coming back down to earth with a bang.’’