The Edinburgh outfit drew first blood over the Accies in their two-legged battle at New Douglas Park thanks to a double from teenage striker Jason Cummings.
After the match, manager Butcher was in a buoyant mood as Hibs saluted for the first time in 13 matches ahead of the return bout at Easter Road on Sunday.
"It was very pleasing," he said. "We didn't know what to do because the half-time team talks 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."
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