“I’m over the moon,” said Reitan. “It happened way sooner than I would’ve imagined. Absolutely thrilled, awesome experience and very grateful.
“There are a lot of pieces that have to fall in place. There’s a whole puzzle that needs to shape up and I’ve made some steps in multiple areas of the game.
“A big one is the belief that I can do it.”
Fitzpatrick won the Zurich Classic with his older brother Matt last month, which earned him a two-year exemption on the PGA Tour.
He then finished in the top 10 at the Cadillac Championship and was one stroke behind Reitan before his second double bogey of the day on the par-three 17th.
Compatriot Tommy Fleetwood finished in a tie for fifth on 11 under after closing with a two-under 69.
Fitzpatrick, the world number 120, told Sky Sports: “It’s still very surreal [to be in contention]. It’s crazy to feel disappointed but I still am.
“I’m happy for Kris, he deserves it, and hopefully it’ll be mine another time.”
Fitzpatrick felt “one bad swing” cost him on the 17th after he had recovered from a “slow start”.
He added: “I’m disappointed not to have won, but I’m also really proud of myself for how I battled out there.
“I was three over through three and then in my head I’m thinking I could shoot 81 here. So I was super happy that I was very patient.”
World number four Matt Fitzpatrick finished on one over after a final round 72, while Northern Ireland’s Rory McIlroy bounced back from a 75 on Saturday to finish with a 67 on five under.