The former English men’s amateur champion had five birdies in his two-over-par round and was one under after 15.
But his second shot to the 16th left him with a hanging lie in a bunker that left him no option but to play into the middle of the hazard.
He failed to get up and down in two and, after responding with a birdie at 17, also double bogeyed 18 after tangling with both fairway and greenside sand.
“Overall there were a lot of positives, but sadly they are overshadowed at the moment by the poor finish,” he said. “There’s so much sand in the bunkers, and it’s so sticky, unless the ball’s entering from the top edge anything from the side just sticks on the side.
“On the 16th I had to hit it into the middle of the bunker – I couldn’t go sideways or backwards – for my third shot.But five birdies out there was pretty good.
“Those who went out two to four o’clock had it as good as it got. When we went out it was still a bit blustery and a bit cold for the first five or six holes then we started warming up.
“It would be nice to have a few more shots to play with.”
By the time he tees off in the second round in the penultimate group at 4.05pm, the EuroPro Tour player may find that his position has improved without striking a shot.
While appreciating the experience of playing in his first major, Dean also shows a demeanour that augurs well for his future as a tournament player.
He has girlfriend and two-handicapper Emily Lyle caddying for him to share each memory.
But he said: “It was an amazing experience, but at the end of the day it’s a job.
“It didn’t really feel like we were out playing in the Open. It just felt like a normal round of golf.
“I was saying to Emily on the way round, the course is so hard you never get away from yourself.
“In the EuroPro events there are always two or three holes that aren’t gimmes, but they give you birdie chances. Here you have to hit really, really good shots to get a chance.
“It’s good in one sense because you never get out of the moment, you never get ahead of yourself because you’re always thinking about that one shot.”
Moortown’s Nick McCarthy has two fewer shots with which to manoeuvre after a four-over par 74.
After birdieing the third to compensate for a bogey at two, he shed four further shots without making any gains.