Interim boss Kennedy was left rueing a series of "big chances" that went begging while United keeper Benjamin Siegrist was also in top form.

Kennedy said: "Everyone's disappointed. Us as much as the fans.

"It's been a rough season and ultimately we have to face up to the fact we have not been good enough this year and Rangers have been better than us and that's why Rangers have won the league.

"We've had such a long spell of dominance not just in the league but other competitions as well and this is a setback for us.

"We can't stand back and feel sorry for ourselves and think, 'oh well that's gone'. We have to keep driving forward.

"There is the Scottish Cup to play for and for players in the squad it's about moving forward to next year and the next challenge."

Asked what needed to happen at the club for next season, Kennedy replied: "That's a decision for the board and how they structure things and what they want to change. But ultimately it's about having the core group there and adding to that and getting better and improving."

The former Celtic defender however, urged caution against wholesale changes.

He said: "I think there is always panic in these moments, it can be very emotional at times, especially in the city of Glasgow where it is always Celtic and Rangers.

"When ones wins and the other doesn't there is a setback and everyone gets so concerned by it, " said Kennedy, who welcomed the return of James Forrest as a second-half substitute after being out since last September with an ankle problem that required surgery.

"Yes, there have been concerns this year that we have to address but massive overhauls don't often work so we have to be stable in terms of the end of the season.

"We know what we have to fix and we have to make sure we fix it."

United boss Micky Mellon's eighth-place side now have no realistic chance of making the top six but he was pleased with his side's performance.

He said: "Celtic have unbelievable talent. We have group of players who are working hard, we coach them and coach them and it is a triumph for coaching and hard work from a group of players who went out there with the right mentality to try to get a result.

"Sometimes you have to celebrate that as well, not just go on about Celtic had this and that.

"Of course we had to understand that we had to be very good in the 18-yard box, we had to be aggressive and make sure we limited Celtic but they were relentless, they kept getting to the ball all through the game.

"Yes, my keeper had to make some saves but that is what he is there for, so they weren't good enough to beat him."