The Premier League visitors to Turf Moor needed two second-half spot kicks to beat the Championship leaders, with Dyche disagreeing with referee Robert Madley's award of both.
"I asked the referee and he said he was happy with his view; I wasn't as happy with his view," Dyche told reporters.
"I think it's a very difficult position to see a penalty from. He's behind the play and three or four players, but I always respect referees' decisions and that's the way it is.
"There was no major contact, certainly not enough to bring them to the floor, but the referee has to make a decision and he's made one."
The defeat to the Hammers was Burnley's first in nine matches in all competitions.