Corine Remande, 49, was hit by the three-time major winner’s tee shot at the sixth hole at Le Golf National in Paris in the opening session of the match.
Koepka, who is in Scotland this week for the Dunhill Links Championship, released a statement through social media on Tuesday night saying he was “deeply hurt” and “saddened” by the incident.
Speaking in St Andrews this morning, he said: “It’s sad and I am torn up about it. I’m heartbroken, I’m all messed up inside.
“In my career it will be the one shot I definitely regret even though everyone from the Ryder Cup and the PGA of America have assured me she will get the care she needs.
“Yesterday was one of the worst days of my life. I haven’t had too many tragedies in my personal family where there has been a loss or any accident.
“I’ve been lucky in that sense and I wasn’t told until I got to the golf course. I’m not the biggest guy on social media so when I got here and 25 messages I was heartbroken.
“My stomach sank and yesterday was probably one of the hardest days of trying to focus on playing golf, knowing what is going to come.”
He added: “We reached out to Mrs Remande and her husband to see how things are going and we didn’t hear back last night.
“I’m looking forward to speaking to her today or in the next few days because there is nobody who feels worse about this than I do.”
Asked what his message to Mrs Remande would be, the US Open and US PGA champion replied: “I’d like to keep that personal between me and her and I don’t see why it’s anyone else’s business.
“It’s sad she won’t see out of her eye ever again. It’s upsetting, it really is, I hit a golf ball and someone lost their sight in their eye.”
The incident has led calls for spectator safety at golf events to be reviewed.
“The European Tour and the PGA Tour do an unbelievable job on the set-up but unfortunately we can’t always hit the fairway every time,” continued Koepka.
“That’s the worst part. Now I can see why we take it for granted every week how courses are set-up and why.
“The set-up on both tours is unbelievable but the sad part is it seems every week someone gets hit.”