The three-times world champion, who won gold in Beijing by more than a minute, missed out on the team for London with Beijing bronze medallist Emma Moffatt, Emma Jackson and Erin Densham selected instead.
The 30-year-old's appeal, on largely technical grounds, was heard on Monday with the Olympic Appeals Tribunal concluding that "there was always going to be one exceptional athlete disappointed in the outcome."
"Whilst I am upset with the outcome, I have to respect the decision of the tribunal and will not be pursuing the matter further," Snowsill posted on her website.
"I would like to again apologise to those affected by my appeal and to thank the other athletes for their discretion in the matter.
"My appeal was never a criticism of their abilities and I sincerely wish them all the best for their preparations and performances in London."
The women's triathlon at the London Olympics will take place in Hyde Park on August 4.