Jason Tovey and Sam Hidalgo-Clyne pegged back the hosts, but after going scoreless in the second half until the 77th minute, there was no way back for Edinburgh and Munster leapfrogged the Scots into sixth place.
And despite moving back into the all-important Champions Cup places, Ireland international Stander is calling on his side to tighten up their defences ahead of their final game at home to Scarlets.
"It's good to get the tries but I think it's the small stuff we need to fix, that they can't get the points on us," the 26-year-old told RTE Sport.
"The lead in the first half was good but it would be better if we didn't give them points.
"We needed to come out in the second half and score points but we played to the end, and that's a thing we've missed all year.
"I'm proud of the boys for coming out and getting their tries.
"The focus going into the Scarlets game is going to be fixing our defence and play our game. There's all week to concentrate on what we can do and what we can control."
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