Defeat for St Mirren at Kilmarnock meant Inverness were on the brink of safety after goals from Filipe Morais and Dougie Imrie cancelled out Brian McLean's opener for Motherwell.
But John Sutton levelled to leave Caley Thistle just three points off the bottom with two games left.
Butcher was unaware his side were so close to sealing their top-flight status until after the game.
"The players' heads are down because we got ourselves in a good position," Butcher said. "But a point is a good result here at any stage of the season.
"I wish I knew we were so close to safety but I don't think it would have made any difference, and I don't think you can relay that to the players as they have to concentrate on the game."
The former Motherwell manager admitted it would have been special to seal their safety at Fir Park but he added: "I don't care where we do it as long as we do it.
"John Robertson said something good at the weekend, which is unlike him, that we were 'tiptoeing' to safety. We're taking small strides instead of big ones.
"We've got ourselves into good positions to take those big strides. It's frustrating.
"We scored two great goals and conceded two sloppy goals, so that's very disappointing. But there was a lot of heart there."
After sealing seventh place, Motherwell manager Mark McGhee may give some of his players an extra week off following Saturday's trip to Hamilton, if last-day opponents Kilmarnock secure their safety this weekend.
Well helped their bid for a Europa League place via the Fair Play league by picking up no bookings and McGhee is thinking ahead to their possible July 2 start next season.
"That's the best we can do after the split so I have got to be pleased," McGhee said.
"I can give one or two a bit of a rest if Kilmarnock are safe.
"If that's not the case then the others expect me to put out my strongest team and we'll continue to do that."