Skipper Jason Forster added: "We did try to play, but things just didn't come off on the night. They scored tries off our mistakes and that's all they needed. There is a good feeling in the squad, though, and we're looking forward to going to Edinburgh next. We're confident of pulling things around and getting the win."
Munster fly-half Ronan O'Gara limped from the field in the first half with a serious-looking knee injury, but that was the only bad news for the Irish side. O'Gara opened the scoring with a ninth-minute penalty goal, before a late Sweeney effort levelled the scores at 3-all at the break.
The stalemate was broken in the 57th minute when Munster backrower Alan Quinlan bustled his way over the try-line under the posts from close range. Replacement fly-half Paul Burke added the extras, and Munster started twisting the knife. Winger John Kelly scooped up a loose pass to scamper over untouched, and the 3-all deadlock had turned into 17-3 within the space of three minutes.
Kevin Morgan scored his 10th League try of the season after some good work from centre Sione Tuipulotu, but the game was Munster's shortly afterwards. Fullback Shaun Payne showed great pace to beat Morgan to a Burke grubber kick, and referee Rob Dickson gave the former Swansea man the benefit of the doubt in the scramble over the line.
Newport Gwent Dragons:
Try - K Morgan
Pen - C Sweeney
Tries - A Quinlan, J Kelly, S Payne
Pen - R O'Gara
Cons - P Burke 3
Halftime: 3-3 Referee: Rob Dickson (Scotland)