Following a lean period in front of goal, Hibs have now scored five goals in their last two matches ahead of Thursday's visit of city rivals Hearts.
Butcher, who replaced Pat Fenlon in the dugout in November, 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.
A minute's silence was observed before kick-off after Hibs Under-20 player David Paul died suddenly in his sleep last Sunday.
Butcher added: "We wanted it because of the poignancy of the situation. A lot of David Paul's family members were here.
"It was a special day on Thursday (in the win at Ross County) but we wanted to make it extra special against Kilmarnock."
Following his side's 4-0 Boxing Day thrashing of Hearts, Kilmarnock manager Allan Johnston was disappointed to leave Easter Road with nothing.
He said: "Hibs made it difficult, especially in the first half. They were right on top of the second balls.
"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.
"It's disappointing to lose a goal from a corner, especially with somebody getting a free header.
"It's disappointing and all the players are disappointed to lose such a soft goal to start with.
"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."