I recommend crediting the author of the edit in your own edit summary, and maybe even including a link to the rejected edit. In future similar situations, the edit summary could be:
applied author's edit I accidentally rejected: URL
author with the actual username of the author, or with an anonymous user, or similar, if it was an anonymously submitted edit.)
But some people really dislike long-ish edit summaries, so if you happen to be one of those people, this is sufficient:
applied author's edit I accidentally rejected
This is what I've always done, when I've made this mistake while reviewing suggested edits on Ask Ubuntu. It seems to have worked well. It gives credit where credit is due and documents what happened, and then I can basically forget about the whole thing (just reminding myself to try avoiding the mistake, of course) and go about my day.
The key point is that you're making clear that the edit is not your own work. This is a best practice generally (avoiding plagiarism and maximizing integrity), and may also help to mitigate any bad feelings or--perhaps even more important--any confusion that may have occurred from the review itself.
As for the question of whether or not there's a better way that editing the post yourself at all: No. Usually you don't have the ability to efficiently ask the editor to resubmit the edit. If they did then other reviewers might make the same mistake. And in any case most people aren't in it primarily for the +2, so asking them to resubmit the edit so it could be accepted a second time would just be heaping more work on them to fix a problem they were uninvolved in causing, rather than fixing it yourself.
In conclusion, I think you did the right thing, except that next time I recommend making clear in the edit summary that the edit did not come from you. (Remember, edit summaries are seen by anyone viewing the post's revision history.)