Acknowledge, but don't argue with, the negativity on the platform it was presented. Some say a "thank you" is the right way to go, some say "I'm sorry" is better. I say it depends on what's being said, but you need to acknowledge it.
Offer several contact methods that you will respond to (on the platform used) – in order to get the hater to contact you so you can fix the problem. You'll show your other customers that you are willing to try, even for folks who are shy about sharing their information.
If you're given the opportunity to fix the problem – and you often won't be – then fix the problem. Simple as that.
Thank them for the opportunity to resolve the issue (on the platform used) – if you are allowed to fix the problem and you do fix the problem, thank your customer for the opportunity to fix the problem.
Reach out one more time – If you're not given the opportunity to fix the problem, give it one more try. Make this a week to 10 days after the problem was reported, just in case the person is there. Repeat your contact info and be available to fix.
Never mention the problem again (but continue to monitor the page each week) – You had the last word, so you're done. But you still want to monitor the page, so look every three to five days to make sure nothing new has cropped up.