Billy McKay's opening goal was cancelled out by Josh Magennis' double but Gary Warren drew the away side level before McKay's second goal won the game for Butcher's charges.
"We were joint-bottom of the league on four points with Dundee at one point. We've come a long way in a short space of time and it's all down to these boys," said Butcher.
"It was a poor first half today. It took us a while to get into our stride, and it certainly wasn't pretty.
"Aberdeen changed their shape for the second half and it actually suited us better. We were able to cope better with how they played in the second half.
"Unfortunately we went a goal behind, but we showed great resilience and character to come from behind, and they've shown that all season."
Butcher admitted he would have been happy to settle for a draw when they came back to 2-2 but his players were keen to push for the winner.
"I did say on the bench I would take 2-2 when we equalised," he added. "The players came over and said 'We can score more goals here' and the chances they made, we could have scored more.
"We've gone to both of the top two now, and beaten both of them on their own patch. It's a great story.
"Even at the start of the season when we were drawing and losing games, we knew we weren't far away. They're an incredible bunch of players."