The dressage rider failed to grab the elusive 11th medal and was forced to settle for bronze in the Grade IB individual freestyle event.
"Some people might not believe me when I say this, but I was genuinely upset that Lee did not draw level with my tally of 11," Grey-Thompson wrote in The Telegraph.
"Regardless of what happened to Lee on Monday, he was already a huge success in his own sport, and in my view winning nine golds from his first nine attempts elevated his achievements above others. I won 16 medals from 21 attempts.
"Lee is also a friend, which made me all the more upset on his behalf. He will be disappointed for himself as he sets himself very high standards but he has no reason to do himself down. Nobody trains harder in his sport and he always goes out to win."
Grey-Thompson is known as the most decorated British Paralympian following her successful stint as a wheelchair racer.