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Munster stayed in touch and after Stephen Fitzgerald's second-half try brought them back into the contest, Stander smashed over from close range to leave Ospreys with just a losing bonus point.
Steve Tandy's side have now lost three in a row in the GUINNESS PRO12 for the first time since the 2012/13 campaign and surrendered their 14-match unbeaten run at the Liberty Stadium, but Rees believes he saw a marked improvement after their opening 28-6 loss to Ulster.
"It's been a hugely disappointing start obviously, losing two games and with the points as it is," he said.
"We have concerns about that, but what we have to say is that the disappointment this week is different to last week. We didn't turn up last week whatsoever, but against Munster the boys did give us the effort, application, enthusiasm and a basic understanding of what we're trying to do.
"So we've got to encourage what we've got this week, and take some learning around a really raw group which included a lot of debutants and inexperience.
"The signs are there and we'll take that on towards Edinburgh. Physically we were at the races and we challenged on first phase, and defensively we were off the line and there was abrasiveness along the contact area to us.
"But the result will linger and it's hard to put into words [how disappointing it is to lose on the final play]. Munster have stolen the victory and good on them, but it really hurts the manner in which we have had to take that."
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