The Owls continued to press but Burnley held on for all three points.
Dyche said: "It was another performance with good productive moments. I don't think it was as good as we have played and we were close to playing well in the first half. We scored two very good goals I must say, very good bits of quality.
"In the second half we knew they would come back at us, they've got a big physical presence and we had to match that or be better than that.
"I felt the biggest turning point was an unbelievable not given penalty which, quite frankly, if we score then I think that's the game done and it flattens the crowd. Over a season you hope there's a balance of it, but it changed the feeling of the game.
"They came back at us stronger, got it forward even quicker and we had to make sure we dealt with it and overall we did.
"In the end it was a small moment in a big game but it could have been a big moment. Another big moment was Tom Heaton's double save, so I'm very pleased with that as well."