Celtic manager Brendan Rodgers conceded his side have made a disappointing start to the season after they slipped to a second defeat in six games, losing 2-1 to Kilmarnock.
Leigh Griffiths gave the champions the lead after 34 minutes at Rugby Park but, after Chris Burke's equaliser half an hour later, Celtic were undone by as stoppage-time winner from Stuart Findlay.
The result leaves the Bhoys fifth in the table after six games, six points behind league leaders Hearts, who beat Rodgers' men 1-0 earlier in the season.
"It hasn't been a great start to the campaign but we have to accept that," Rodgers told a post-match news conference.
"We're the only ones who can make it better by playing better and getting more consistent results.
"It's been very bitty but we have to go away and work and see where we can be better."
Celtic meet St Johnstone in the League Cup on Wednesday before entertaining Aberdeen at Celtic Park on Saturday, and Rodgers believes fatigue from Thursday night's 1-0 victory over Rosenborg in the Europa League may have been a factor.
"I take responsibility," he added.
"We made the changes to try and get that energy and brightness and sharpness that may not be there if you've played late on a Thursday night.
"I'd have been disappointed to draw the game but to actually lose is bitterly disappointing."
