While your question can be improved upon I can understand the difficulty in finding the words.
I believe that your use of "sorry" might be fairly described as more of an interjection, yet saying that would not help another understand.
Other approaches: something that you did not mean to be taken literally would be to say your meant something 'figuratively'
figuratively from Merriam Websters online
a : with a meaning that is metaphorical rather than literal
Speaking of panic, I recently ran into (figuratively, not literally) a friend who was ranting about giant "bees" digging holes in his lawn. —Ron Kujawski
Poor small-town America. During the last gasps of this fevered election, pollsters, zealous campaign foot soldiers and reporters are kicking down its doors, figuratively speaking … —Doug Colligan
Now, strictly speaking, you did NOT use the word figuratively, but because we understand figuratively to basically mean ~not exactly what it means~, I think the word would make the general point.
Another way of describing your use would be to call it a 'rhetorical flourish'.
We most commonly think of "rhetorically" describing question you do not mean to have answered, but if you had said,"I meant the word 'sorry' rhetorically", I think that would also get the point across that the word wasn't meant to be taken strictly.
rhetorical from Websters
1 a : of, relating to, or concerned with rhetoric
b : employed for rhetorical effect; especially : asked merely for effect with no answer expected
for your example
I meant the word "sorry" more figuratively.
I meant 'sorry' more rhetorically.
Apologizing for wording is always awkward though - eliminating the 'I'm sorry' interjection probably would be a good speech habit. (it can come off as less-confident or alternatively a bit patronizing)