Anthony Martial finished off a rapid break to open the scoring on Sunday, with United captain Wayne Rooney poking home a rebound to wrap up the points before the interval.
Burnley failed to record a shot on target for the first time at home this season but the manager was happy with the mentality of his team, despite ruing the goals conceded.
"They are very strong, tactically, technically and with game knowledge," Dyche said. "We huffed and puffed and stuck at it.
"They scored two poor goals from our point of view, we have to make a foul on the first one.
"We stuck at it. I am pleased with the mentality of the second half. They killed the game. They are a top side. That is the reality of playing some of the top sides. You can't always get above where you are."
0 - Burnley failed to land a shot on target in a PL home game for only the 2nd time in their history (also v Liverpool in Dec 2014). Blank.— OptaJoe (@OptaJoe) April 23, 2017
A run of one win in their last 11 Premier League matches has left Burnley five points above the relegation zone but Dyche is refusing to set a target for Burnley in their last four games.
"Until the moment it is all done we will keep fighting and see what we can get," Dyche added.
"Who knows what [how many points] we will need."