The Dragons proved mighty effective for the first 50 minutes but once Andrew Coombs and Jevon Groves were binned in the space of a minute the home side made superior numbers count to send Peter O'Mahony over for a decisive try.
A heavy penalty count hindered the Dragons but Director of Rugby Lyn Jones put on a brave face and was encouraged by his team's battling performance.
"It is so easy to reflect after that and say, 'yeah, we got beaten 23-9', we were outplayed, but it was not like that at all," he said.
"We were better than Munster in lots of areas. They are trying to develop a new type of game, but we dealt with that no problem. Munster had to go back to their old stuff, the tight stuff to get what they wanted from the game and they did well.
"But it's hard enough to play against Munster with 15 than to go down to 13 within the stroke of a minute. We are improving but our lineout was off the mark. It cost us dearly, Munster's first try came from a turnover lineout in our own 22. And you can't afford to do that."
Kris Burton traded two penalties with Munster's JJ Hanrahan in the first half to keep the Welsh region in the hunt but the home side edged in front five minutes from the break when James Cronin crashed
Burton pegged back the lead with an early second half penalty but the double yellow card signaled the end of the Dragons challenge as Munster closed out the game in a real arm wrestle.