Just four days on from posting his best major finish at Royal Troon, Horschel was due to return to action on Thursday in the PGA Tour’s 3M Open in Minnesota but withdrew because of illness.
The 37-year-old held the 54-hole lead at The Open but was powerless to stop Schauffele, who carded a six-under 65 to add the Claret Jug to his US PGA Championship win in May.
While Horschel remains disappointed that a couple of poor shots prevented him from putting more pressure on Schauffele, he says he is proud of how he handled the pressure of contending at a major.
“I’m happy with how I handled Sunday. The nerves I thought I would have weren’t there,” he added.
“I felt very comfortable in that arena in that moment. Unfortunately, I missed a short putt at eight and made a bad swing at 10. Other than that, I played really good.
“I would have had to play spectacularly to chase down Xander, he played an unbelievable round of golf.
“Disappointed, when you have a chance to win a major and don’t get the job done it hurts a little bit. But I can hold my head up high knowing I didn’t lose the tournament.”
The 2024 Irish Open takes place 12-15 September, with McIlroy, Horschel and Shane Lowry among the notable players in the field, while Sweden’s Vincent Norrman is the defending champion.