Ashley Barnes grabbed the winner for the visitors.
Dyche said, "We showed a good mentality towards the game. We were 1-0 down and there was no panic.
"We had calmness and the belief is growing again in what we do. We scored a really good goal and then the sending off changes the feel of the game. Then it is difficult. It is game of patience and believing we will break them down and we did.
"We stayed focussed, shifting the ball and eventually scored with a really fine move."