American skier Lindsey Vonn says she has “no regrets” after a crash in the women’s downhill competition at the Winter Olympics resulted in a “complex tibia fracture” which will require multiple surgeries.

The 41-year-old’s arm got stuck in a gate just 13 seconds into her run on Sunday at Olimpia delle Tofane in Cortina, throwing her off balance.

She was treated on the slope for a lengthy period before being airlifted off the piste to Ca Foncello hospital in Treviso, where she had surgery on a fractured left leg.

The 2010 Olympic downhill champion was already racing with ruptured ligaments in her left knee but was determined to compete in her fifth and final Games.

“Yesterday my Olympic dream did not finish the way I dreamt it would,” she said in a post on Instagram on Monday.

“It wasn’t a story book ending or a fairytale, it was just life. I dared to dream and had worked so hard to achieve it.

“While yesterday did not end the way I had hoped, and despite the intense physical pain it caused, I have no regrets.

“Standing in the starting gate yesterday was an incredible feeling that I will never forget. Knowing I stood there having a chance to win was a victory in and of itself.”

Vonn crashed in Switzerland in the final race before the Olympics nine days before competing in the downhill event in Italy.

In a media conference on Wednesday, she confirmed she had torn her anterior cruciate ligament (ACL) but expressed determination to compete.

The two-time world champion says the torn ACL and her previous injuries, including a partial right knee replacement, “had nothing to do with my crash whatsoever”.

Vonn’s decision to race has led to widespread praise for her bravery but also criticism about the dangers and potential risk of permanent damage.

“It always was and always will be an incredibly dangerous sport. And similar to ski racing, we take risks in life,” she said.

“We dream. We love. We jump. And sometimes we fall. Sometimes our hearts are broken. Sometimes we don’t achieve the dreams we know we could have. But that is also the beauty of life; we can try.

“I hope if you take away anything from my journey it’s that you all have the courage to dare greatly. Life is too short not to take chances on yourself. Because the only failure in life is not trying.

“I tried. I dreamt. I jumped.”