The answer to your question of what to do in this case is don't worry about it and do nothing with the answer - focus on writing more good questions and answers.
You answered the question and it was accepted by the OP. Great, that means you solved the problem, and got some rep from that! But, your answer got a downvote. It would be great to find out why! It looks like it may have been because your suggested course of action is unclear. In which case, you should clarify it. A lot of times, reading the comments is a useful thing - it helps give you guidance towards what may be wrong. Sometimes there are no comments; it never hurts to ask people "Hey, I'm getting downvoted, can someone perhaps explain to me what's wrong" in your own comment on your answer.
Your answer is pretty good, though the specifics about what you are proposing may appear unclear for users, and you may need to clarify more specifically why you're proposing the answer you did. (Even though it's accepted by the OP and solved their issue)
In this single case, though, you've only got a single downvote. Don't fret, we all get our posts downvoted at some point or another!
My advice, in detail:
Do not remove your answer, which actually helped the OP. This is the first thing you need to care about - did your answer actually help the OP, and if it did and they accepted it, it's unlikely you'll want to delete it, in case it helps others with the same problem. Even if the system permitted you to do this, you should do a lot of thinking before deleting posts - it's not the best solution to things.
Also, don't delete things that aren't absolute junk - your answer doesn't qualify as junk, so unless it's flat out wrong you should leave it be.
Don't worry about downvotes and reputation points so much. Regardless of your reputation level.
Reputation points are only there for the purposes of showing contribution and gaining privileges the more you contribute positively. If you continue to post good questions and answers, you won't need to worry about losing a small number of points from a downvote.
What you should worry about is when you start getting a bunch of downvotes on a specific question or answer (but not getting all your posts downvoted in a suspicious way). If you start getting these, and it's not because of serial downvoting, then it's possibly a problem with your answer - whether quality of the answer or accuracy of the answer, or whatever. That's when you should re-evaluate your answer - see if you can make it more clear, or update it if the solution is outdated.
A side note on worrying about downvotes though - if your posts get serially downvoted by a voting ring in an abusive format (and I mean beyond that which you could expect from an unclear or wrong answer), contact a moderator to look into whether this is a serial downvoting situation. The system (and us moderators) have tools and procedures for handling these cases, and one of the things we're here to do is make sure these things aren't happening, because we don't like people abusing the systems.
- Just keep posting good questions and answers! This is the best thing you can do - one or two downvotes are not something I would worry about, because posting more good questions and answers will get you reputation to offset a couple of downvotes. Reputation is also not necessarily the driving force for posting on Ask Ubuntu - your primary drive should be to help others, and to ask good questions and provide good answers, not worrying about every single point of rep you have.