Hibs needed to win on Saturday to avoid the two-match showdown for top-flight survival but, with only one win in 18 games since January 2, their limitations were once again ruthlessly exposed at Easter Road.
"We were well on top in the first half and they get one chance and it's in the net. It just would not break for us," Butcher said.
"We've hit the bar and had loads of incidents in front of goal but it just never fell our way.
"Fair play to Kilmarnock. We're just missing a striker like Leigh Griffiths, a man to put the ball in the back of the net."
When asked for his reaction to fans calling for his head after the final whistle, Butcher said: "I still see myself here but we've got two games to try to rectify the wrongs of the previous 38. There have been some highlights in those 38 games but not many.
"We have to keep going. We are not relegated. We have two games left to make sure we stay in the Premiership. We've got 10 days until the first play-off match.
"You feel like you've been slapped in the face. I can only apologise to the fans - we put them through the wringer. We always seem to be coming in at half-time 1-0 down or 2-0 down. It's just not happening for us.
"We had injuries to the spine of the team. Paul Heffernan got injured. We've not had him a lot of the time. When you get into a rut like we have been, it's hard to get out of it.
"I am absolutely committed to the club. The fans were great, they really got behind the team. It can't be the usual story in these next two games."