The 27-year-old Englishman carded five birdies in a four-under-par 67 that lifted him to five under for the championship.
It was a contrast to Saturday when Pepperell felt he squandered some good opportunities as he followed up opening rounds of 71 and 70 with another 71.
He said: “I was a little hungover. I had too much to drink [Saturday night].
“I was so frustrated with [Saturday} that Sunday was – I wouldn’t say a write-off, but I didn’t feel as though I was in the tournament.
“I just had some wine with my coach. We drowned our sorrows for about half an hour. It was enjoyable. I didn’t really think I had that much to drink. I’m just a lightweight”
Pepperell admits his approach to this week’s tournament, which did not involve a practice round, was “very, very casual”.
He said: “I wouldn’t always have a drink the night before, sometimes I have a few.
“It depends how you feel. I’ve done it all different ways. It depends on how you feel. I like to socialise in the evenings if I can. It takes some of the sting out of competitive golf at this level. It’s stressful.”
Of his final round, Pepperell said: “It was tough, hard work. Just getting the ball to the hole felt hard. I managed my game exceptionally well.
“I knew on certain tees I wasn’t going to hit good tee shots, so I played for the rough and missing bunkers. This course lends itself to that in those conditions. Had this course been wet, I wouldn’t have had much joy, but I managed my game well enough to post a decent score.”
Pepperell’s fellow Englishman Tommy Fleetwood insists he does not want to be a “baby” about his Open finish, but accepts he should have done much better.
A birdie at the first to get him to six under, just three behind the overnight leaders, was greeted with a huge roar, but he just could not get it going and his hopes went the way of his ball when he smashed it out of bounds at the sixth.
The Southport golfer finished three under – five behind champion Francesco Molinari – and was left frustrated after a runners-up finish at the US Open a month ago.
“I don’t want to be a bit of a baby about it, but I’m obviously disappointed,” he said. “I didn’t really feel like I did that much wrong. Could have got it going because the crowd were with me.
“It was just the middle of the round that got away, but the story of the score is I still had a chance and just couldn’t do it.
“I could have done things better this weekend, but it just wasn’t to be.
“I felt like I did so many things right, but putts just didn’t really drop for the weekend like they did the first two days and overall that was it.
“It’s always sad and disappointing, but it just wasn’t my time.”