The 46-year-old looked well placed to book his berth after opening with a four-under-par 68 at West Lancashire, one of four Final Qualifying venues for The Open.
However, a disappointing three-over 75 in his second round saw the 2017 Masters champion tumble out of contention, finishing well outside the five available places.
Garcia later explained that he started to feel ill during the day after eating something which did not agree with him.
"I had a little bit of food there in the players' lounge, and it did not sit well with me. I only ate the lasagna. It didn't sit well with me, and I just felt nauseous the whole front nine. In the afternoon, I felt like I was going to vomit pretty much on every hole," he said afterward.
"When you're this age and you're playing 36 holes, you feel like you need to eat a little bit between the rounds, and you do that and it doesn't sit well with you and you're struggling with your stomach pretty much the whole second round; it's tough. You come all the way here to give it your best shot, and not feeling 100% there… it hurts a lot."
Former Masters winner Danny Willett and fellow Englishman Matt Wallace also fell short at West Lancashire, where Sheffield's Sam Bairstow claimed medalist honours on 10 under par.
Joining Bairstow in qualifying from the venue were New Zealand's Kazuma Kobori, Spain's Jose Luis Ballester, Germany's Tiger Christensen and England's Matthew Jordan.
At Dundonald Links, Scotland's Jack McDonald earned top spot on five under par, with England's Matthew Baldwin, American Marcus Plunkett and amateurs David Howard and Nevill Ruiter also booking places in the field.
At Burnham and Berrow, there was another American success story as James Nicholas led the qualifiers. Fellow Americans Caleb Surratt and Austen Truslow also progressed, alongside England's Tom Sloman and Spanish amateur Alejandro de Castro Piera.
South Africa's MJ Daffue secured his place at Royal Cinque Ports, where England's Matthew Southgate, Denmark's Bard Bjornevik Skogen, American Peter Uihlein and France's Antoine Rozner also advanced.