Richie Foran opened the scoring in the fourth minute and Billy McKay's 36th minute strike sealed a third straight win to keep Caley at the top of the Scottish Premiership table.
Butcher said: "It was a good first half performance, but I felt that overall it was a game of two halves.
"We knew that with the wind in the second half Motherwell would get it forward to John Sutton, while they have good pace in their team.
"They caused us problems, but we defended well and showed a lot of grit, resilience and steel.
"That's the new mantra at this club - stamina, steel and style."
Motherwell's defeat was their second in succession and boss Stuart McCall was left to bemoan his side's poor start.
He said: "We talked before the game about settling into the match, but then we find ourselves a goal down after four minutes.
"I thought that the tempo of the first half just wasn't good enough, so there's a lot of work to do.
"The second half from us was better, but it had to be.
"I thought they had the most outstanding player on the pitch in Richie Foran. He defended set pieces in their box, he won tackles in the midfield and scored a goal.
"It was a really disappointing performance and result. We have to show a bit more than we did against Inverness."