Captain Jon Daly's last-minute penalty came after the Tangerines had raced into a 3-0 lead inside eight minutes - before Billy McKay's hat-trick followed by Gary Warren's 86th-minute header looked like earning the points for the second-placed visitors.
"It was an absolutely incredible game," said Butcher. "After eight minutes I'm thinking our run is over because our game-plan was gone. We had to change things round and got into the game so I can only give credit to the players for doing so."
He added: "We got two goals back from Billy McKay's opportunism after United had made a blistering start.
"In saying that, we compounded that by throwing in some goals as well with some poor defensive play. Our team talk was quite simple as well at half-time because we treated it as though we were only 1-0 down.
"I must stress our team played a tough 90 minutes in the Scottish Cup against Ross County during the week so their fitness levels are excellent. I'm so pleased with their spirit and commitment but we were just disappointed not to hold on for a win in the end.
"It was one of the most exciting games you'll ever see in the SPL. It was end-to-end-stuff. There were incidents galore and penalties which made for great entertainment so everyone got their money's worth."
Meanwhile, Dundee United boss Peter Houston admitted his side were reeling from throwing away a three-goal lead.
Houston said: "It feels morel like a defeat if I'm being honest. When you go 3-0 up so early on in any game and score goals at home you really do expect to win the match
"The only thing I'm pleased about is the fact we got a late penalty to get us a point."
- Sports & Recreation