Dyche's men gave an impressive account of themselves at Old Trafford, quickly levelling through Danny Ings - who became Burnley's record Premier League goalscorer with his ninth in the top flight - after Chris Smalling had put United ahead.
The visitors then had chances to forge ahead but instead paid the price for their profligacy as Smalling restored United's advantage in first-half injury time.
Robin Van Persie wrapped up the points for the hosts with an 82nd-minute penalty, leaving Dyche to bemoan what might have been.
"I thought the quality, particularly in the first half, was outstanding," he said. "Everyone in the stadium was probably scratching their head at how we didn't come away with anything.
"There has to be a future in what you're doing. There is definitely a future in our last two performances, we're sure of that.
"To come to Old Trafford and play on the front foot, with the energy and the quality we did, I think shows what we're trying to be about this season.
"We're frustrated we haven't got more wins, we're frustrated we haven't got more points, but I think with that kind of performance, there's a future in that.
"You have to win, you have to get points, that's the job."
Dyche also reserved particular praise for Ings, whose form in front of goal is keeping Burnley in with a fighting chance of Premier League survival.
"I thought Ingsy was first-class," he added. "Their players will know about him after tonight. He's a very, very talented player in my opinion.
"I thought he was excellent - his movement, his energy, his will, his quality. All the things that you want out of a player."
