Michael Higdon netted a double - the first a tap-in on the half-hour mark and the second a wonderful first-time volley from the edge of the box in the 56th minute.
Nicky Law grabbed the second with a typical burst into the box and good skill and persistence and Motherwell enjoyed a comfortable last half-hour.
Inverness suffered their fifth defeat in six matches and failed to bounce back from Wednesday's 1-1 draw with Kilmarnock, when they lost a last-minute equaliser after dominating.
Butcher had been generally pleased with their form before their trip to Fir Park - but he was not happy after this loss.
"We were second best," he said. "They showed more hunger and appetite for the game and got the goal at the crucial time.
"I thought we started the game very well. You could see our lads were a little bit leggy after the midweek game, they put a hell of a lot into the Kilmarnock game and there was a lot of heartache when we didn't win the game.
"There have not been many times we have come up second best against a team and unfortunately it has always been Motherwell.
"The pivotal moment was the first goal, we defended like amateurs. It gave them a lift and knocked us back."