Shane Long won and converted an early penalty in Saturday's Championship clash at Turf Moor after being brought down by Leon Cort, and Jobi McAnuff grabbed a deserved second just after the break.
Cort was then sent off for a second yellow card before Michail Antonio and Simon Church ensured Reading claimed their first win away from home since a 2-1 victory at Leicester in August.
The Royals boss said: "I'm delighted with that. To come here and win at Burnley, who are unbeaten at home this season is a great achievement.
"I thought our shape was good and we thoroughly deserved to win the game.
"We made a great start and it was a definite penalty. I didn't know whether (Cort) was going to be sent off or not because (Long) was in on goal, but he wasn't.
"We had opportunities to make it 3-0 and we didn't but when it came the third goal killed it off."
Reading lost 1-0 at home to Swansea last weekend and then suffered the same fate at Bristol City in midweek.
McDermott admitted it had been a tough seven days for his side, who are now just a point behind today's opponents in eighth place.
"I'm just pleased with the way we performed," he added. "We came out with a clean sheet against Burnley who are going to be there or thereabouts at the end of the season.
"You can see that they've got quality players.
"I was just pleased that after back-to-back defeats we managed to get a win.
"It's never easy when you lose to Bristol City on a Tuesday night. But we've got that out of our systems now and we'll focus on Doncaster.
"It was important today that we bounced back and we did that."
Burnley boss Brian Laws, who watched his side lose at Turf Moor for the first time this season, was at a loss to explain the defeat.
Only Bristol City had prevented the Clarets from winning at home this season before today.
Laws said: "It's a difficult one to put your finger on, other than to say we've got to be totally honest with ourselves and say we weren't good enough.
"I've also got to give credit to Reading for doing a job on us.
"I just thought there were so many performances that were below par. You can live with one or two, but when it's half a team you get a kick up the backside.
"The performance certainly doesn't measure anywhere near what we're capable of.
"I could excuse the referee who I thought had a difficult game, but I thought the players were worse than that."