Two first-half goals from the prolific Billy McKay helped Butcher's Caley Thistle side to an ultimately comfortable 2-0 victory over Hearts in the Scottish capital, to keep Inverness at the top of the table.
It was a game the Jambos would finish with 10-men, with captain Jamie Hamill receiving his marching orders for what seemed a harsh handball inside the box, although McKay missed the subsequent penalty.
But despite Inverness dominating the contest, particularly in the second half, Butcher saw enough from Hearts to suggest that they can continue to overcome the minus 15-point deficit handed to them at the start of the season for going into administration.
He said: "We managed to beat a good Hearts side. Even before a ball was kicked this season, I felt that Hearts could stay up.
"They have a good spirit about them and if they can keep everyone fit then they've got a chance.
"We named the same team for the fifth match in a row and if Hearts can try to do that as well then I'm sure they can do well."
After a run of three Scottish Premiership games without defeat, Hearts missed the chance to close the gap even further on fellow strugglers St Mirren and Kilmarnock, but manager Gary Locke was remaining upbeat.
He said: "We have to remember that Inverness have had a really good start to the season, so we can't let our heads go down.
"Inverness are a good, experienced team, while we are coming here with a lot of 17- or 18-year-olds.
"Before the game we lost a couple of players to suspension that have been influential, so that made it difficult for us."