Burnley had opportunities to take the lead and were denied numerous times by Dimi Konstantopoulos in the Boro goal in the second half.
"Our fans have seen a dominant performance, but I've not seen so many decisions go against us in a long time," Dyche told reporters following the game.
"The stats were through the roof, with 27 shots and 71% possession. It's just a shame the officials didn't have a good game today.
"The shirt pull on Danny Ings is incredible & there was at least one other factual penalty. But you need the rub of the green sometimes."
Burnley return to action next Friday when they take on Blackpool.