The Hoops looked on course for all three points at Rugby Park after Leigh Griffiths fired Rodgers's side into a 1-0 half-time lead.
But Chris Burke equalised for Killie on 64 minutes, before Stuart Findlay, who began his career with Celtic, nodded home a last-gasp winner.
Findlay got the run on Boyata in order to head home in the dying stages, and the Northern Irish boss has lamented his side's defending.
He told The Glasgow Evening Times: "The second one is basic. You have to defend a corner and be strong but Findlay gets in front of our guy and you’re disappointed.
"I’ve been there when we’ve scored enough late goals and it’s always sore when you lose it late but we’ve got no-one else to blame but ourselves."
He didn't name him, but Rodgers's use of the phrase 'our guy' suggests that he was talking about Boyata, who was in no-man's land when the goal went in.
The Belgium international, who earns £14,000 per week in Glasgow [Daily Star], has been excellent for the Bhoys when he has played this season, and was fine for the most part yesterday, but he was undoubtedly sleeping late on and Findlay made him pay dearly.
Have something to tell us about this article?