The home team have developed defensively since Butcher arrived at the club in November, but Butcher was frustrated by the bluntness of his attack in recent games.
But an assured Hibs deservedly claimed the points with goals from Paul Hanlon, Paul Cairney and Lewis Stevenson, while Kilmarnock goalkeeper Craig Samson kept them at bay son several occasions as well.
Butcher said: "We encourage shots in training and we stop the training sometimes and say, 'why don't you shoot?'
"I think they're just starting to get around to the fact that it's quite fun. No-one is going to give them a rollicking if they miss the target or don't score.
"The more shots you have the more chance you have of scoring; the more crosses you have the more chances you have of scoring.
"That's what happened here, we pressed on to them. Craig Samson made some unbelievable saves in the first half."
Killie manager Allan Johnston reckons his team deserved more from the match and was frustrated to lose a goal from a set-piece.
"Hibs made it difficult, especially in the first half. They were right on top of the second balls," He said. "We knew the dangers they've got, scoring two goals from corners at Ross County.
"They had not been scoring a lot of goals recently. We knew that was going to be the danger.
"I don't think there was much in it between the two teams and in the second half we dominated spells. At 1-0 you have to learn that you're still in the game and you cannot get caught on the counter-attack.
"We ended up getting beaten 3-0 and it looks like we have been thrashed when there was not much in the game."