A win over Dundee United on Saturday for Butcher's men would have nailed the desirable third place, but an injury-time strike from Gary Mackay-Steven saw United win 2-1 at the Caledonian Stadium.
And as it stands, depending on Sunday's result, Inverness, St Johnstone and Ross County are all still in contention for the remaining spot.
But Butcher said: "There is huge disappointment because we have had enough chances to win two or three matches.
"We missed a penalty as well. It's our fault that we're not in Europe now. It's as simple as that.
"I don't think we deserved to lose the game but you've got to put the ball in the back of the net from chances and we had chance after chance after chance and missed.
"We were going for the winner. We kept going but then of course they hit us with the sucker punch."
Inverness face the possibility of taking on local rivals Ross County next week in a bid to wrap up third place, and a win for County against Motherwell on Sunday would keep their hopes of European football alive in the lead up to the derby.
Butcher said: "We said before today's game that if we didn't win it would all come down to next week.
"We will look forward to that game but it's a hard one to get over at the moment."