"It feels like a victory in many respects," Butcher told BBC Sport. "It's about spirit and togetherness."
"It's great spirit, determination and perseverance from the players. They kept going, and I don't know how many crosses we put in the box and how many corners we had.
"If you keep going and keep going, and there's a belief there, sooner rather than later you'll get something from it."
Hibs continue their Scottish Premiership campaign next Saturday when they make the trip to champions Celtic.