The Hoops were unable to recover from a 2-0 half-time deficit as Steven Davis' overhead kick and a Jonjoe Kenny own goal sent Rangers through to a quarter-final tie against St Johnstone and kept the Ibrox men on course for a double.
Odsonne Edouard missed a second half penalty as Celtic passed up a catalogue of chances in their attempts to salvage the tie – and their season – but Kennedy stressed that the damage was inflicted in an unassured opening 45.
“I’m disappointed. It’s a competition we wanted to keep a hold of in terms of another trophy. We were confident going into the game but that didn’t come through in the game, especially in the first half and our approach to the game," he said.
"I thought we were a bit too passive in the first half in terms of how we pressed the game and passing the buck a little bit and not taking responsibility. We addressed that a bit at half-time but you then come out and you have given yourself a lot to after conceding two goals.
"We came out much more aggressive and we created big chances. If we had taken one of them at 2-1 you have given yourself a chance but we didn’t manage to do that again. We just have to take it on the chin. It will sting a bit and we have to deal with that.”
The defeat leaves Celtic trophyless for the first time in a decade but Kennedy refused to question the mentality of his squad.
“They are a great bunch, I have no issues with them at all. Even today, in terms of being cautious in the first half it wasn’t down to a bad attitude or not wanting to run and work we were just too tentative. There wasn’t full belief," he said.
"When we showed that in the second half we created chances but by that point it’s 2-0 and when you don’t take the big chances it dents the confidence again and we have had numerous hits like that this year. Again we have to get over that by making sure we represent ourselves properly going forward, and see where it goes.”
With another Old Firm fixture just two weeks away – a dead rubber league match with the title already decided – and a new manager appointment on the horizon, Kennedy is preparing for a summer of change.
"We know the mentality of the players, and we know there might be gaps in the summer. There will be players coming in and out and they have a terrific attitude," he said.
"I can't put a number on it but in terms of the squad we need to add to that.
"We have lost a couple of players, a couple might be coming out of contract, these decisions will be made in the summer.
"I don't want to overly talk about it.
"We are losing our captain Scott Brown, Soro is in the building but we need to add to that.
"So there will certainly be changes, maybe a little more than we normally do."