St Johnstone's defeat at Celtic earlier in the day meant a win for the Highlanders over Dundee United would have secured the coveted third spot in the Clydesdale Bank Premier League.
But an injury-time strike from Gary Mackay-Steven saw the Taysiders grab the 2-1 win instead - their first victory since the league split.
As it stands, Inverness, Saints and Ross County - depending on their result on Sunday - are all still in contention for the one remaining Europa League berth.
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."
Billy McKay failed to convert from the penalty spot before Aaron Doran fired Inverness into the lead just before the break.
United were back on level terms through Ryan Dow early in the second half, leaving the home side with no option but to throw men forward in search of the winner. But it was the visitors who were celebrating when Mackay-Steven had the net bulging at the end.
Butcher added: "We were going for the winner. We kept going but then of course they hit us with the sucker punch."
Inverness now face the prospect of taking on local rivals Ross County in Dingwall next week in a bid to finally wrap up third place.