Despite clinching the SPL four weeks ago, Glasgow Celtic manager Neil Lennon was disappointed that some of his players were in "holiday mode" at Tannadice.
Scott Robertson's header in the 21st minute was the only goal of the game as Dundee United took maximum advantage of Celtic's hesitancy.
Lennon wasn't happy with Celtic's display. "It's a disappointing result. I thought we should have won the game. Our play in the final third was poor in terms of the final pass and finish.
"I don't remember my goalkeeper having anything to do and the goal was poor, because we switched off to allow a player who was five foot ten a free header six yards out.
"I can't remember the last time we conceded from a corner - it summed up the day - I wasn't happy with the attitude of some of the players, some of them are in holiday mode already. The major disappointment for me is that we've lost our unbeaten record in the league."
Lennon felt Celtic's approach and finishing work could have been better. "There were too many touches on the ball, taking too long to get the ball forward.
"United had a game plan to sit back and we had all the play. But, having said that, we missed good chances.
"In that aspect, we were creating good chances, but we didn't have the final finish, but overall I can't criticise the players too much over the way they've played over the last six months."