But she said her mind was changed by a stranger whose sister died as a result of "COVID damage".
Garraway – whose show is nominated in the Authored Documentary category – wrote on Instagram: “Have been feeling very torn about asking you to vote for our documentary #FindingDerek's nomination for @officialntas tomorrow.
“I am very proud of it but felt I shouldn’t be asking for more from you.
“I have even wondered if I shouldn’t go to such a sparkling event and take time away from the family who need me now more than ever.
“But a stranger just changed my mind! She was walking past our house & called out, 'hope you win'. I thanked her but said didn’t think we would as so many good ones in the category & I hadn’t been campaigning for votes as others have.
"She looked horrified. 'But you must,' she said. 'My sister died from COVID damage two weeks ago. Her heart had been ruined by the virus last summer. She watched your documentary and it gave her so much hope.'
"It broke my heart."
The TV star went on: "So now I am asking you to vote please – not for me but to highlight the thousands that have lost lives and livelihoods to COVID, and to the thousands more that battle on devastated by it.
"Also for the millions of others who are facing terrible diagnoses of any illness, the tortuous wait for treatment as our NHS strains to cope.
"It would be wonderful if your vote meant they felt less forgotten and helped me to fight on for them."
Draper returned home in April after spending more than a year in hospital after contracting the coronavirus, and now needs round-the-clock care.
Speaking on This Morning, Garraway said at first she was not even going to go to the awards, which take place on Thursday night (9 September), because she felt sad about not being able to go with him.
"I just felt very very sad this week," she said.
"January 2020 when we were all at the NTAs, the last time it happened in that way, I was able to go on stage because of I’m A Celebrity if we can even remember I was ever in the jungle.
"I can remember thinking, I wish I hadn’t left Derek babysitting. I wish I'd said, 'Come', because I just had this weird feeling that something might not be as great again, not knowing anything of what was coming.
"In my mind I always thought, well if we ever get to go again, if the world ever edges back towards normal it would be so wonderful if he could go, and it's so obvious that he can’t.
"And I just felt very sad about that."
Draper and Garraway tied the knot in 2005 and have two children – son Billy, 12, and 15-year-old daughter Darcey.
Joining Finding Derek in the newly-created Authored Documentary category is Katie Price for her film Harvey And Me, which documents life with her son, who has numerous disabilities.
Watch: Kate Garraway goes on first night out in 17 months