Butcher's team had numerous chances before and after Nick Ross scored from close range following an Aaron Doran cross in the 21st minute.
But they did not take any of them and had to settle for a point when Borja Perez scored with Kilmarnock's first shot on target in the closing stages.
Butcher said: "I'm bitterly disappointed.
"We dominated the game and, if it was a boxing match, Kilmarnock would have been counted out.
"I expect my back four to hold out and not dive in.
"That was their only shot on target and we have had countless chances to win it, to say I'm disappointed is the understatement of the year."
Kilmarnock boss Kenny Shiels said: "I think we deserved it because we showed a great desire and commitment to get something from the game.
"Inverness missed a few chances but you have got to give our players credit."