Hill, 35, struck out nine and threw 89 pitches before being taken out.
Roberts said he understood why Hill, who was visibly upset in the dugout after being pulled, would be so emotional.
"I feel sick to my stomach," Roberts said. "I am going to lose sleep over it tonight."
Roberts said that Hill, who had spent time on the disabled list this year with groin and blister injuries, started to develop a tender index finger on his throwing hand.
"As a manager, you take in a lot of information," Roberts said. "It was in the best interest for him, his finger, and the Dodgers."
After the game, Hill said he understood his manager's rationale.
"Looking at it from a team aspect, there is always something that is bigger than any player," Hill said. "You have to understand that."
Hill added that his finger felt fine.
According to the Elias Sports Bureau, it was longest perfect-game bid in the modern era (since 1900) by a pitcher who was removed from the game.
The Marlins ended up with two hits in their losing effort.
It isn't the first time this season the Dodgers have pulled a pitcher who had yet to yield a hit during the game. On April 8, Roberts pulled rookie Ross Stripling from a no-hitter after 7 1/3 innings pitched in a 3-2 loss to the San Francisco Giants. The bullpen also gave up two hits in that game.
Left fielder Yasiel Puig made an outstanding diving catch for the final out of the seventh. Martin Prado hit a drive to deep left-center and Puig sprinted after it. As he approached the warning track, he dived toward the wall to make the catch about 355 feet from the plate.
Hill entered the game a combined 11-3 with a 1.94 ERA in 16 starts this year for Oakland and the Dodgers, who acquired him on Aug. 1. He has just three complete games in 91 big league starts over 12 seasons.
Information from The Associated Press was used in this report. ESPN's Doug Padilla contributed to this report.