Hearts' David Smith had cancelled out James Collins' opening goal before Liam Craig's late penalty gave the home side their first win over their City rivals this season at the third attempt.
"Ten points out of a possible 12. That's pretty good form. We know we can be better but we are delighted with the result," Butcher said.
"It's our first league penalty of the season and it was nice to see Liam tuck it away. I think he is our eighth goalscorer, while I've been the manager. He was calmness personified.
"I thought we thoroughly deserved to win the game. You have to win a derby and send the crowd home happy. The stadium was bouncing. It was a fantastic atmosphere.
"I told the players to relax. When we did get the ball down and pass it we did pretty well. We feel we should have scored more goals. At the back Paul Hanlon was absolutely immense. Their goal came out the blue, against the run of play.
"We have set something in motion here and it's going to get bigger and bigger. We will get more quality in. We are on a great run and we want to keep it going.
"Up front we know they could get more goals but they work their socks off. People think it's easy, that you go home and have nice glass of red, but you don't. I have 18 DVDs of Dundee United to watch!"
Hearts manager Gary Locke was not so enamoured with referee Bobby Madden as he saw his slide slip 16 points adrift of Ross County.
With the scores locked at 1-1, Jordan McGhee was penalised for sticking out a leg as Lewis Stevenson chased a lost cause and Craig won the day from the penalty spot.
"We got a decision from the referee that has cost us a couple of points," said Locke. "From where I was there didn't look a lot in it.
"That sort of thing happens every week. There's not a lot we can do about it. I was hoping in 2014 we might get the rub of the green from the officials but it hasn't started too well for us. It seems to be big decisions go against us at the minute.
"I am very disappointed for our fans that it was a controversial decision that has cost us. We needed people to their bodies on the line and they did that.
"We have to start winning games. It's been a disappointing weekend for us, with Ross County winning."