Sandwiched between the two home draws were a 0-0 draw at Liverpool and a 4-0 defeat at Chelsea.
United's third draw in 10 games left them in eighth place, on 15 points from 10 games. Manchester City top the table on 23 points ahead of Arsenal and Liverpool on goal difference.
Herrera said Burnley should have been on the received end of a heavy defeat given the number of chances United created.
"We controlled the game for 90 minutes. Not to score a goal was unbelievable," Herrera told British media.
"We have the luck against us right now but we have to keep playing like we did here and against Stoke and hopefully one day we can get a fair result - 5-0 or 6-0."
Herrera was shown a second yellow card against Burnley for a clumsy challenge. It was the Spaniard's first sending off since moving to the English top flight.
"The first yellow card I bent my knees, I didn't want to kick the opponent," he said. "The second, I slid in. But I don't want to complain because I don't want to be banned for more games," he added.
"The only thing I can say is that I didn't want to make those fouls. I am not a violent player. I slipped."
(Reporting by Ian Rodricks in Bengaluru; Editing by Peter Rutherford)
