Richie Foran took advantage of some lax defending to head home an early opener but Kilmarnock came out in determined fashion after the break to level within five minutes, although there was a touch of fortune about their goal as Graeme Shinnie's clearance bounced off Barry Nicholson and in.
Kris Boyd hit the post from an improbable angle but Kilmarnock otherwise struggled to break down a dogged Inverness side as the visitors defended their lead.
Butcher's voice was hoarse from shouting at his players throughout the game but he was happy to see his side fight for victory.
"It certainly wasn't one of most fluent performances of the season but we weren't allowed to play in the second half," he said.
"Fair play to Kilmarnock, they had a lot of possession and put us under a lot of pressure but Dean Brill has not had a lot to do in the second half.
"It was more a resilient, gritty, hard-fought game. I would love to have played in that myself. The ball has been taken to hospital because it's been battered and bruised.
"Billy's goal was crucial. They got the equaliser and the momentum was with them and a long ball over the top, Billy latches on to it and it's a goal.
"Billy was adamant he was onside but we will have to wait and see. The service he got in the second half was awful but he made the most of it and worked his socks off."
Butcher's post-match summary showed the standards they have set in the past 14 months and this season in particular.
He said: "After the game, Maurice (Malpas, assistant manager) said to the players: 'Hands up who played well?' And not one of them put their hands up.
"We asked them if they enjoyed the game. They enjoyed the three points.
"I could really hammer the players today and say: 'That wasn't good enough'. But I can't do that because they are a lovely bunch of guys and they know they haven't played well.
"But we still held firm, we still made sure they didn't have the chances to nick it, and we have always got Billy McKay. So it's not a bad little formula."
The defeat left Kilmarnock still without a win under Allan Johnston and he has to continue dealing with familiar frailties as he bemoaned the lapses of concentration that cost them.
"The first half we did all right at times but the second half I thought we came out and played really well, and lost a really soft goal after getting ourselves into a strong position," he said.
"I sound like a broken record, but we can't afford to lose goals as easily as that. The first one is from a throw-in and all it is is the second ball. And the second one is just a long ball over the top and we have to deal with it better.
"You have got to learn, you can't keep on making the same mistakes because you can't afford to (need) two and three goals to win a game of football.
"The boys know the mistakes they are making, we have shown them and been over them in training."
Johnston, who started with Jeroen Tesselaar and Jackson Irvine in central defence, added: "Darren Barr's wife is in labour and he had been at the hospital all night so someone like that is obviously a big miss as well."