Alpine skier Vonn, who won the Olympic downhill title at Vancouver 2010, ruled out any chance of a defence in Russia as she continues to battle back from ten months out with a knee injury.
Alcott herself is on the comeback trail, first breaking her leg in Lake Louise in 2010 before pulling out of last season's World Championships injured and then suffering a re-break in August.
Speaking in a column for the Evening Standard, she is targeting a run at the World Cup in Cortina d'Ampezzo, which begins on January 16, but Alcott expressed her sadness at Vonn's fitness failure.
Alcott had just completed a training run in Austria pain-free as she bids to make her fourth Olympic appearance at the Sochi 2014 Olympic Winter Games, which begin in less than a month.
And she said: "My day yesterday was in total contrast to that of Lindsey Vonn, who has had to withdraw from Sochi with her own injury problems. I'm absolutely gutted for her because I know how hard she had worked to get back in time.
"It's a race against time to get there but that has been the case since I broke my leg on August 23. Yesterday, though, was different. I felt fast, I felt right in every way imaginable.
"At the bottom of the mountain there was no emotion, there's no time for that, but there was happiness and satisfaction at what I'd done.
"There I was skiing pain free. Okay, you always have a weird feeling with a large piece of metal in your knee but the important part is there was no pain."