At points though, the Ospreys let their opponents back into the match, Munster scoring nine points without reply to get back from 13-0 down to 13-9.
And although the win was welcome relief after the Liberty Stadium outfit lost their first three games of the season, Rees still believes they aren't at their best.
"We showed some slight progression from last week," he said. "There was lots of positive intent as there always has been, but we showed more common sense.
"We were good in terms of physicality but there were a few dodgy periods when we had a bit of looseness about our game - we still need to go up another notch.
"We were pleased tactically with the first 25 but were disappointed with the last 15 going into half-time.
"We spoke honestly with the players that we needed to sharpen up, which we did to a certain extent in the second half, but there were opportunities we didn't put away.
"We look at our average points per 22 entry and it's not anywhere near where it should be at the moment. That's a big focus for us in training.
"It was perhaps different to a traditional challenge against Munster but the boys known they've been in a hell of a game.
"I think it's a promising season for Munster, they are still riding high in the league and I sincerely believe they'll be up there in Europe as always.
"It's another building block for us, but in Italy next week we need to be better.
"Our physicality and directness has got to come to the fore, not just next week in terms of our performance, but also as a launch pad for the weeks afterwards."
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