The National League West-leading Dodgers (42-25) went on to capture a 2-1 walk-off victory when Dee Gordon smacked a two-out single off Matt Thornton in the 10th inning.
"Anytime you lose a game, it [stinks], but especially when the starting pitcher throws as well as [Quintana] did," Reed said. "I made a couple bad pitches and they hit them and it didn't work out."
The White Sox (35-31) turned to Reed after the rookie Quintana threw just 77 pitches in a career-high eight innings. In the no-decision, Quintana struck out a career-high six, walked none and allowed five hits.
"He pitched great, but right there, I wanted to go to our closer," White Sox manager Robin Ventura said.
Against left-hander Thornton in the 10th, Gordon came up with his second career walk-off hit for the Dodgers' sixth walk-off victory of the season. Tony Gwynn scored on Gordon's hit after Gwynn's one-out triple eluded diving left fielder Jordan Danks.
Danks said he was trying to make an aggressive play.
"Just a hair short," Danks said. "It landed in front of me. Just my killer instinct told me I could catch the ball. Came up short."
The Dodgers nearly tied the game in the sixth, but an official ruling erased the run. On an appeal, Matt Treanor was ruled to have tagged and left third base too early on a potential game-tying sacrifice fly to right field. The tying run was wiped from the scoreboard.
Dodgers manager Don Mattingly was ejected in the top of the seventh after protesting the call. He argued with third-base umpire Jerry Meals and then with home-plate umpire Gary Darling. It was Mattingly's fourth ejection this season and seventh as Dodgers manager.
"When they tell you they got it 100 percent right, it's hard to buy that," Mattingly said. "I understand close calls and bang-bang and you can't see things, and trying to see that at fast speed is different than replay. It's hard for me to believe you can overturn a run if you are not 100 percent sure you got it right."
Ventura said the White Sox appealed the original call based on timing.
"You look at where a guy is at, looking over there when [right fielder Alex] Rios was catching," Ventura said.
The appeal and dramatic rally punctuated a pitchers' duel. Quintana threw his first scoreless outing as a starter, lowering his ERA to 1.53.
"He's going against some really good teams and pitching well," Ventura said. "It's not a fluke."
For the Dodgers, left-hander Chris Capuano struck out a season-high 12, one short of his career high. He allowed a run and six hits, walked one and threw 111 pitches.
The White Sox's Tyler Flowers struck out four times, and Adam Dunn struck out three times.
"He seemed to do a lot of the same things Quintana did, didn't make mistakes over the plate," Flowers said of Capuano.
Dayan Viciedo's two-out RBI single off Capuano ended the scoreless tie in the sixth. Brent Lillibridge scored after leading off with a single, moving to second on a fielding error by left fielder Herrera and advancing to third on a groundout.
Sunday concluded a three-game series that involved three one-run games. The White Sox have lost nine of their last 14 games and hold a 1 1/2-game lead over the Indians in the American League Central. They begin a three-game series against the Cubs on Monday night at U.S Cellular Field.
"We're just going to go out there tomorrow and forget about today and get after it," Reed said.