Dempster picked up the decision after the Cubs' 6-3 win over the Pittsburgh Pirates, but he wasn't happy when informed after the fifth inning by Quade that he was coming out of the game.
"I think it's just because the cameras are there [that it's a story]," Dempster said. "I think guys used to do that all the time.
"The bullpen pitched so much [recently], I thought I could do a better job of throwing less pitches. I wanted to get deeper in the game. That was more of my concern than personally being out there."
Dempster, who missed his previous start because of back pain, threw 87 pitches. He was touched for three earned runs and struck out four.
"I might prefer that we take care of things up here [in the clubhouse]," said Quade, who's in his first full season as a major league manager. "Sometimes these things happen.
"If it happens because he's [ticked] off because he's a competitor, I'm OK with that. He's earned the right to do that from a veteran's standpoint. If it was a kid that did that, it might be something else."
Dempster was animated while exchanging words with Quade in the dugout before the two headed into the tunnel leading to the clubhouse.
Quade said the two didn't talk after the game and probably won't until Sunday or after the All-Star break.
"No we didn't talk. He had to go up and do what he had to do," Quade said. "I had a game to manage."
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.