Dempster said it's up to Zambrano, who is still waiting to find out how long he has been suspended by the Cubs, to help his teammates move past the incident.
"I think that's up to him," Dempster said Monday on "The Waddle & Silvy Show" on ESPN 1000. "When you do those things and react the way he did you have to be the one to stand up and go out there and accept responsibility. I think he will be willing to do that but we'll have to wait and see. I can't make speculations because I don't know what's going to happen. Whatever happens, happens and we're just worried about going out and winning the ball game tonight."
Cubs left fielder Alfonso Soriano agrees that Zambrano needs to address the team.
"I think he needs to apologize, because it wasn't good for the team," Soriano said before Monday's 2-1 loss to the Pittsburgh Pirates at Wrigley Field. "I think we need an explanation about what he did Friday."
Zambrano, who is three years into a five-year, $91.5 million contract, is 3-6 with a 5.66 ERA and recently rejoined the starting rotation after spending five weeks in the bullpen.
Zambrano further angered the Cubs when he went out to dinner with White Sox manager Ozzie Guillen hours after his tirade. Cubs general manager Jim Hendry and Piniella expressed their frustration with Zambrano's decision over the weekend, but Dempster said it didn't bother him.
"Me? Would I do it? No. But to each their own," Dempster said. "When you're away from the field you can go hang out with whoever you want to hang out with and have dinner with whoever you want to eat with. I know [Zambrano and Guillen] are really good friends away from the field, and they talk a lot and they see each other a lot in the offseason. He's free to do whatever he wants."