Teenage striker Jason Cummings scored both goals at New Douglas Park to leave Hibs in the boxseat ahead of Sunday's return leg at Easter Road.
The victory was Hibernian's first on the road in 2014 and Butcher admitted he was unsure of what to say to his players at the final whistle.
"It was very pleasing," he said. "We didn't know what to do because the half-time teamtalks don't normally revolve around a 1-0 lead.
"Then, after the game with a 2-0 lead, I thought, 'Wow, what do we say?' You come in with total disbelief.
"But it is a lovely feeling. We haven't had this feeling for a long, long time and it was great to send the Hibs fans away happy, which is what we always want to do.
"It is weird in many aspects because there is still another game to go.
"The opposing manager is saying it is not over and I am definitely saying it is not over and the players are saying that too.
"There is still a lot of work to be done and we have seen that Hamilton are a good side. We have to have the same focus and attitude on Sunday."
Asked about the selection of 18-year-old Cummings, who was signed from Hutchison Vale Boys club last summer, Butcher added: "It is was a gamble in many ways as he hasn't scored for the first team but he has played really well.
"To score two goals like that, all credit to him. He has a lot of confidence and talent, he is a good prospect."
Hamilton player-manager Alex Neil was disappointed his free-scoring side failed to find the net and admitted his side must improve if they are to overturn the two-goal deficit in the second leg.
"I thought we dominated the first half, we played well and created good opportunities and then found ourselves down to Hibs' first shot on target," he said.
"I don't think we merited a 2-0 defeat. We lacked a bit of quality in the final third which is unusual for us.
"It is difficult now. We have to perform as well as we did but take our chances. That was the biggest difference in the game."