McIlroy described the abuse as “unacceptable” and said it should be “off-limits”.
Sprague says he plans on apologising to McIlroy and his family.
“I haven’t spoken to Rory or Erica [McIlroy] but I do plan on sending them an email with my heartfelt apologies because of what occurred,” he said.
McIlroy suffered lengthy abuse before eventually snapping by swearing at a spectator that called out while he was addressing the ball.
“I chirped back because it got to me a few times, but we tried to handle everything that came our way with class and poise, and for the most part, I felt like we did that,” said McIlroy.
“It was a rough week for all of us. But at the same time, we shut them up by our performance.”