Heike Holstein finished sixth in her group on board Sambuca in the dressage event on Sunday with a score of 68.432.
Competing in her fourth Olympic Games, Holstein and Sambuca were placed into Group D where Denmark's Carina Cassoe Kruth came first with a score of 76.677.
The top two from each group, as well as the six highest scores who haven't already qualified, secured a place in the individual final, meaning Holstein and her mount missed out.
"I was really happy with her, she went into the ring and really concentrated," Holstein said of her 12-year-old mare.
"We had a few little errors that were my fault, in the first medium trot I had her back a bit too much. I was really happy with the passage and the piaffe has improved a lot, she was really relaxed in the walk and the changes were good.
"I timed the warm-up just right, I practiced it yesterday at the same time and I had more time today so I did less with her before I went in. She wasn’t exhausted but wasn’t too fresh. I was happy with most of it.
"I am really proud of her. When she was a little foal I never thought that we would get this far, it is a long road and lots of things can happen. In 2019 I finally thought this might happen."
Holstein wore a yellow ribbon in memory of Tiggy Hancock, a 15 year-old from Bagenalstown in Co Carlow who died in a training incident last month.
"Tiggy is at the Olympics in Tokyo and we are very proud to wear this for her."