Cirrus Des Aigles' trainer Corine Barande-Barbe said it was a privilege to have a horse good enough to be a worthy opponent to Frankel.
"I'm feeling great. It was an honour to meet Frankel and I am very proud of my gelding," she said.
"I think we brought Frankel an international line and he defeated a horse who won in Dubai, in Ascot and in Longchamp.
"It was a great day and it was just like a victory for us just to have the horse to make Frankel gallop.
"There are no regrets. We are proud to give the challenge and show our horse is now the best in the world when Frankel goes to stud."
Cirrus Des Aigles could now have another crack at the Hong Kong Cup in December with Barande-Barbe keen to give her stable star another chance at the mile and a quarter feature after he was fifth in the race last year.
"He'll probably go to Hong Kong. I saw him after the race, he looked great," the French handler told At The Races.
"My staff told me this morning he has eaten everything and is still happy and enjoying everything. I will give him a week to see how he is."
She also intends to have another go at the Champion Stakes, which he won in 2011, next autumn.
"We will probably come back again next year," she said.
