The 27-year-old failed to qualify for the final of the 25 metre pistol, finishing 37th out of 39 with a score of 562.
But while she is disappointed, Okehampton-born Geikie has completed a lifetime ambition and is now turning her attention to the next Olympics.
“It was my life ambition to get to London 2012 but now I have the t-shirt I want to go on and get a medal in Rio in 2016,” she said.
"I was naturally disappointed. I was unlucky in the precision, scoring just outside of the ten, but this is a precision sport and just outside at this level is not good enough.
"I have had a massive smile on my face. I am the first British pistol shooter to compete for 80 years so I am thrilled, especially as I qualified to compete.
"I completed all my 60 shots and I hope I have done Britain proud. The crowd is amazing – you sense that they are all with you, supporting you all the way."
Geikie is a part-time barmaid to help supplement her income and wants the exposure her sport has received to boost training opportunities and participation.
She said: “It is very hard to train in the UK as there are only two places we can train – in Dorset and Bisley.
“It is tough on us as in other countries competitors can train at their local club. I live in my car and my family have been very supportive.
"This has been a great opportunity to show people what I do and I hope that it will encourage young people to get down to their local club and get fit and take up the sport."