Craig Levein felt Hearts' injury-time loss was a cruel way to finish a hard-fought game in which the Jambos played with 10 men for the entirety of the second-half.
Celtic eventually ran out 2-1 winners thanks to Odsonne Edouard's volley in the 93rd minute.
"It can be a cruel game at times," Craig said. "To lose it, when I felt that we had coped with just about everything that Celtic had thrown at us, is difficult to take. Credit to Celtic, they kept going right till the end and got the win.
"They dug deep for the whole match. We started the game really well and had the better opportunities. We had Celtic pinned back for periods of the game like we've done previously here and I was happy with the way things were going, until the sending off and we fell behind."
Jamie Brandon's 44th-minute red-card threatened to let Celtic romp to victory but the Jambos fought back in the second-half and levelled through Ollie Bozanic's penalty.
"I can see why Steven [McLean] gave it," Craig admitted. "Jamie's elbow is high. I'm not sure how much contact there was, but I can see why.
Levein was dealt another blow at half-time when he had to replace Steven Naismith: "His knee was irritating him a little bit. He wasn't feeling that he was free and could run properly so we don't want to take any risks. We'll investigate that and see what the problem was."
Despite the final result, the manager felt there were many positives to take from the match.
"The players were so diligent in their defending. Celtic had opportunities but they didn't have clear-cut opportunities and anything that they did that got by the defence, the goalkeeper dealt with quite well but you've got to go until the last second of the match and that was proven today.
"In moments like this, we've got to try and look at the positives and take the good things from the game that can give us confidence going into this next run of fixtures."
The Jambos now face Partick Thistle on Monday night in the quarter-final of the Scottish Cup and Craig believes his side can take confidence into that meeting.
"I said to them after the game if you compete and work for each other and do all of the things that we did tonight on a weekly basis, then we will get rewards.
"There are times when you don't get what you deserve from games and you have periods in seasons where you don't get what you deserve but all of the commitment, effort, running and diligence in defending - apart from that one moment - all of those things are good and if we can replicate that in the coming weeks we will be fine."