I saw it through without exemption.

Happy new year to all the teachers.

I am listening My way by Frank Sinatra and wondering the meaning of “exemption” on this sentence. (I did look up the dictionary, but still don’t not really understand the meaning). Could you re-phase it to an easy-understanding version ? Thank you.

“I did what I had to do
And saw it through without exemption.”

I was not freed from the duties of what I had to do. I carried it out, I did not shirk the responsibility or look for a way out of doing it.