Caley Thistle earned themselves a 3-0 win at Ibrox on Wednesday night to reach the semi-finals of the competition for the first time in the club's history.
"I'm absolutely thrilled," said Butcher. "We talked about what it would be like to come here and play, a lot of the boys hadn't been here before.
"It's a fantastic place to play football, very intimidating, but I thought they handled the occasion very well.
"It was an excellent performance and I'm very pleased."
Inverness resume their Scottish Premier League duties on Saturday when they travel to Kilmarnock.