Tamburlini came into the final women's major of the year second in the Ladies European Tour's Solheim Cup points list, with the top two in those standings after this week securing their spot in Anna Nordqvist's side.
The Swiss player arrived at Royal Lytham & St Annes with a slender 1.1-point lead over Helen Briem, with Tamburlini posting a four-bogey finish to her opening-round 75 and confirming her early exit with a three-over 74 on Friday morning.
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Briem and France's Agathe Laisne also missed the cut to end their automatic qualification hopes, but Tamburlini is still left relying on other players' performances over the weekend to see whether she will make her Solheim Cup debut.
"I want it [Solheim Cup spot] so badly but sometimes the things you want so badly almost hinder your performance more," Tamburlini, reduced to tears, exclusively told Sky Sports.
"Obviously really disappointed to not be playing the weekend. I really hope I'll still get the spot and I feel like if I do, it'll be a really good motivation for the next couple of events as well.
"Solheim Cup was one of my goals for this year but it's also my first year on the LPGA Tour as well. Trying to establish myself on this tour has been quite difficult this year, so hopefully I get this spot to give myself a bit of a kick.
"Not looking great as well with keeping my LPGA card at the moment. Worst case, there's always other options as well. I'm trying to take a little bit of pressure off myself with that. We'll see what happens this weekend on the side of Solheim."
The 26-year-old has finished no higher than 17th on the LPGA Tour this season and has now missed the cut in four of her last six starts, although Tamburlini insists her play is better than her 2026 results show.
"I feel like honestly over the last seven or eight weeks I've been really close with everybody in my team again," Tamburlini explained. "I feel like we're connecting more again - it was a bit difficult in the beginning of the year, being more in the US.
"I know the scores don't show it, but I feel like my game is so much more solid. I'm starting to recognize my game a lot more again from how it was the last two years really, which is nice - obviously disappointed to not see the results.
"I feel like my game is, as stupid as it sounds, it's not that terrible really. The margins, we all know it, are so small."
Tamburlini was part of Europe's team trip to Bernardus Golf after the Evian Championship earlier this month, but remains hopeful of returning as part of the 12-strong line-up that takes on Team USA from September 11-13.
"Just being there made me realise again even more really how much I want it," Tamburlini admitted. "It's been nice to get a bit closer to all the older girls as well that I haven't really played with much.
"They've been all super welcoming as well and open for questions and everything, which has been really nice.
Lottie Woad could move above her in the standings with a top-three finish, while Maja Stark and Carlota Ciganda are among the others who could deny Tamburlini an automatic spot over the coming days.
"I will probably end up looking at the leaderboard [over the weekend] a lot," Tamburlini insisted. "Right now, I'm saying my goal is to not look at it too much!"
The Solheim Cup qualification campaign ends on Sunday evening, with the top two on that Ladies European Tour points list by the highest-ranked players available in the Rolex Women's World Golf Rankings earning automatic spots.
Nordqvist will then name her four captain's picks on Monday afternoon, live on Sky Sports. Nanna Koerstz Madsen and Leona Maguire are among the past players in possible contention to be selected, along with former major champion Georgia Hall.
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