The visitors arrived without a win in four and saw that run extended thanks to a fine display from home keeper Tomasz Kuszczak and a single David Lopez goal.
Burnley are seven points off the top six and just nine above the bottom three.
But Dyche said: "We deserved something, absolutely. There is a real positive feel now because we need performances like that.
"You win games with displays like that and to come here and perform like that was very pleasing.
"There were so many good things, like the way we dominated the ball and created chances. It's a positive sign for us.
"The shackles have come off now and the freedom which we showed today will benefit us in the run-in."