The Clarets had gone behind to a clinical Jordan Rhodes strike, but they battled back and skipper Jason Shackell headed them level before the ubiquitous Danny Ings struck the winner.
Burnley boss Dyche admitted that he was never worried about his side going behind.
"I thought the lads delivered a fine performance overall, but credit to Blackburn, they made it very difficult as they would in a big game like this," he said.
"We did not get too disappointed by going a goal down, we still played, we shifted the ball, we still looked to open up opportunities, and I said to them at half-time, you're on the cusp of making history.
"I said don't worry about being 1-0 down, we keep going forward and we keep playing and the mentality we have built as a group here has become invaluable to us."
Despite going eight points clear in second in the Championship, Dyche insists that they are not thinking about promotion.
"It's [the result] only significant because it is another three points and locality of the game but we have another big game coming Wednesday [at Birmingham]. I can [get excited], it is okay for me but the players need to stay calm and focused."
Dyche insists that the result was for the fans, adding: "If you can build that one club mentality and you can galvanise the mentality between players and fans, they know they have players and staff who will give everything."
The Burnley chief was full of praise for match-winner Ings, adding: "Ingsy was outstanding, never stops and always searching for a chance to score a goal and he got his reward.
"A terrific young man, I value him as a person and as a player. It is a big occasion, massive one, but they have handled it and I am delighted for our fans and the board, who are all Burnley fans."
Ings himself said: "It is a massive win, not just for us but for the fans as well - at the moment it is my favourite goal of the season, they all count and I had a chance in the first half I should perhaps have scored but I kept at it and got my goal in the end."
He joined his manager in insisting that they do not want to think about promotion yet.
"We don't want to talk about that, we will take each game as it comes."