Rhys Davies struggles to a 74 in the second round at Turnberry
Rhys Davies said he was disappointed to miss the cut at Turnberry, adding a 74 to his opening-day 73 for seven over.
"I had pretty high expectations coming here, I wasn't just here to take part - I wanted to compete," said the 24-year-old, the only Welshman at the Open.
"It just didn't happen for me and that's frustrating. I'll go back, work hard and try to get to the Open again.
"I'll take some time to evaluate, but I know my game is strong enough at this level, I can only get better."
Davies, from Bridgend, came through a 36-hole event at Sunningdale last month to qualify for his Open debut.
Wales had no representatives at the event last year, the first time that had happened since 1932.
The former Brynteg Comprehensive School pupil enjoyed an outstanding amateur career in college golf in the USA.
He combined his golf with a business degree at East Tennessee University, where local media called him "the best player to ever play" at the college.
In his final year there in 2007 Davies extended his own ETSU record for career individual titles to 10 and became the first UK player to reach number one in America since Graeme McDowell achieved the feat in 2002 while at Alabama State.
Davies turned professional in September 2007 and has made steady progress since, including a second place at the Singha Thailand Open in March, part of a successful stint on the Asian tour.