Johnson highlighted the work of McGee and Portuguese nurse Luis Pitarma after his recovery, saying their care saved his life.
But after being invited to Downing Street for a "Clap for Carers" event, McGee said she wanted to stay out of the limelight.
"It would have been a really good photo opportunity," she said.
"You know, kind of like Boris and his NHS friends, but I wanted to stay out of it.
"Lots of nurses felt that the government hadn't led very effectively, the indecisiveness, so many mixed messages.
"It was just very upsetting.
"Yes, we have put ourselves on the line and we have worked so incredibly hard, and there's a lot of talk about how we're all heroes and all that sort of stuff.
"But at the same time, I'm just not sure if I can do it. I don't know how much more I've got to give to the NHS.
"We're not getting the respect and now pay that we deserve.
"I'm just sick of it. So I've handed in my resignation."
In a statement, McGee confirmed what she told documentary makers.
"After the toughest year of my nursing career, I'm taking a step back from the NHS but hope to return in the future," she said.
"I'm excited to start a nursing contract in the Caribbean, before a holiday back home in New Zealand later in the year.
"I'm so proud to have worked at St Thomas' Hospital and to have been part of such a fantastic team."
In a statement, the PM's office defended the government's handling of the pandemic: "Our NHS staff have gone above and beyond over the past year and this government will do everything in our power to support them."
"We are extremely grateful for the care NHS staff have provided throughout the pandemic in particular."
Sir Keir Starmer took aim at government after McGee's decision was revealed, with the Labour leader saying her decision was a "devastating indictment of Boris Johnson's approach to the people who put their lives on the line for him and our whole country".