The visitors remained undefeated in the capital in the Clydesdale Bank Premier League this season after strikes from Ross Draper and Andrew Shinnie, either side of a deflected Leigh Griffiths goal, were enough to secure the points.
"I'm incredibly happy," said Butcher. "I thought we deserved to win, we created a few chances and could have scored more.
"It wasn't much of a first half, I thought we did OK, but we opened up a bit in the second half and got guys like Andrew Shinnie on the ball more and we felt like we could score.
"We were a bit fortunate with our winner, but Graeme Shinnie was adamant he was pulled down with their equaliser so from our point of view justice was done."
Hibs boss Pat Fenlon lamented sloppy defensive play from his side as the reason they lost a match that he claimed, based on their overall play, they merited taking something from.
The defeat left Hibs in the bottom six with a trip to Celtic Park their remaining fixture.
"I don't think the result was fair," said Fenlon. "Maybe we didn't deserve to win but I certainly don't think we deserved to lose. I thought the work rate was tremendous.
"We had a great opportunity to get a home win and put some pressure on the teams around us and I'm disappointed we haven't done that.
"We gave away two sloppy goals. The first one we didn't defend a straight ball and then with the second goal we defended the free-kick well, but didn't win the second ball. It's not rocket science. The desire not to concede sloppy goals is something we want to get into the team. We need to make teams work harder to score against us."