The 50-year-old Scot, who played in 20 successive Opens from 1990, had high hopes of a first appearance since 2009 after an opening 69 saw him just one shot off the pace at Local Final Qualifying at Gullane.
However, in the afternoon he returned a 76 to slip to three over and with only three places available for Muirfield had to admit defeat.
He was going along nicely in the morning as he was five under through 12 holes but testing conditions made it difficult coming home and the damage of four bogeys in five holes was only lessened by a 15-foot birdie putt at the last.
When he resumed in the afternoon he had every chance to make a push for contention but after a birdie at the par-five third he had four bogeys and a double-bogey six in his next holes to end his challenge.
"I got to five under and threw it away - nevermind," he said.
"It's not my schedule. I just played badly this afternoon [Tuesday]. I didn't get going at all.
"The pace of play was shocking (his second round took four hours and 35 minutes) but that's not the reason I played badly.
"It's very disappointing after being five under."