"Sometimes I felt like a spectator," the defeated third seed told a news conference. "I was close again but I lost it. She deserved to win, she played very well."
Halep, one of the pre-tournament favourites, was beaten 4-6 6-4 6-3, three years after losing another tight final to Maria Sharapova at Roland Garros.
The 25-year-old Romanian, though, was optimistic that her own taste of grand-slam glory would come one day.
"I can just look forward," she said. "If needed I will play 20 years to have this moment."
Halep seemed to be cruising towards victory when she led 3-0 in the second set and had break points for 4-0 but then the unseeded Ostapenko loosened up and fired winners into every corner and on to every line.
"She has great ball-striking ability and when she's hot you don't touch the ball, you become a spectator," Halep's coach, Darren Cahill said of the 20-year-old Ostapenko who hit 54 winners and as many unforced errors.
"You have just got to hang in there and hope she misses enough balls to give you enough chances. That's the way she plays, we've always known that.
"You know that sometimes you're not going to touch the ball."
Cahill, who briefly interrupted his collaboration with Halep this season, citing the player's negative attitude on court, had nothing to reproach her for on Saturday.
"Jelena won this match, Simona did not lose it," the Australian told reporters.
"From our perspective Simona can walk tall, with her head up high; she had a wonderful claycourt season. This will be tough, for sure but I think she will regroup and be a better player.
"I have faith that eventually she will get over it. It's her second grand slam final. Many players before her lost in multiple finals before they finally won and Simona will just have to dig deep and keep working hard.
"I have full faith that one of these days she's going to hold one of those trophies," Cahill said.
(Editing by Clare Fallon)
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