The 23-year-old Northern Irishman, who hit a spectator on the head after going out of bounds at the 15th, said some of his playing rivals needed to put their foot on the gas out on the course.
"This is an issue that has to be addressed because the fans don't want to sit and watch TV and guys not hitting shots and standing over their balls. You want to see it flow," he told reporters after tucking in three strokes behind leader Adam Scott of Australia.
"It's definitely something we need to address because I don't think a round of golf should take over five hours. It would be great if we could speed it up a bit."
Open organisers the Royal & Ancient announced this week they would be cracking down on slow play in the third major of the season but were coy in outlining the specific penalties the players might receive if they transgressed.
McIlroy said he was troubled by the incident at the 15th - where he took a double-bogey six - and delighted with a battling fightback that yielded birdies at the 16th and 18th holes.
"That was an eventful last four holes," he said. "My tee shot on 15 went slightly right and I got an unfortunate break but I thought I did well to keep my composure and keep my concentration and finish the way I did.
"He (the fan) could have headed it the other way, it would have been in the fairway."
McIlroy made amends to the bloodied spectator who quickly had his head bandaged up.
"I gave him a glove with a sad face and my autograph," said the 2011 U.S. Open champion.
"I've done that a few times before, it's not the first time. The most important thing was that he was okay because I would have felt terrible if it had been worse that it was.
"I'm happy with my score. It's a great position heading into the second day," McIlroy said.