The British former Formula One driver suffered two broken vertebrae after a collision with a slower Ferrari at the Sarthe circuit on Saturday evening sent his car flying through the air and into the tyre barriers.
The 33-year-old said he was fortunate not to be more seriously injured.
"I felt I was in an aeroplane out of control," he said in a team Q+A from hospital. "I knew how close the barriers were, and travelling at that speed I was going to be there in no time. That part of the crash was pretty petrifying.
"I felt an almighty punch up my spine when the car hit back down on four wheels," he added.
"I have felt better, that's for sure. I am in a bit of pain, in my lumbar area, the middle area of my back. That's the only thing that hurts really, so I've been lucky."
Doctors put the average recovery time from such an injury at three months but Davidson, a Formula One race analyst for Sky Sports television, said professional athletes could hope to be on the mend much faster.
"It's more like three weeks until the pain subsides and I get my mobility back fully," he said.