Having already landed the Lockinge at Newbury and the Queen Anne at Royal Ascot, the Godolphin-owned four-year-old was a short-priced favourite to complete a Group One hat-trick in Wednesday's feature.
He cut out much of the running before being passed by Here Comes When in the final furlong and while he rallied admirably in the testing conditions, there was a neck between them at the line.
"Ribchester came out of the Sussex Stakes in great form, he's eaten up and trotted up sound," Fahey told www.sportinglife.com.
"It was a strange race. He looked beat - then William Buick said he found his feet again and came home well.
"If a mistake was made then it was probably the decision to make the running - and that was down to me. It worked in the Lockinge, but I probably didn't respect the conditions enough at Goodwood. It wasn't just the testing ground but the driving rain and strong headwind he was running into.
"So we'll look forward now. He's in the Prix Jacques le Marois and another Group One in France on September 10 (Prix du Moulin).
"I've also left him in the Irish Champion Stakes at Leopardstown over 10 furlongs and we could have a look at that, too.
"We'll decide nearer the time."