Rose tore his left ACL on April 28 in Game 1 of the Eastern Conference quarterfinals against the Philadelphia 76ers. He underwent surgery on May 12, and the recovery is expected to take between eight to 12 months.
The Bulls went 18-9 during the regular season and 1-4 in the playoffs without Rose last season.
"We still did good even when we didn't have Derrick (last season)," said Gibson, who threw out a ceremonial first pitch before the Chicago White Sox's game on Monday. "We beat the Heat without Derrick.
"Our mindset hasn't changed. It's about staying focused and taking one game at a time. We understand it's going to be up and down at the beginning of the season. We can't look forward to the end. We got to look forward to one game at a time and playing to our strengths and just listening to coach (Tom Thibodeau). I know it's going to be a long season, but I'm really optimistic about what's going to happen."
Entering his fourth season, Gibson said he and Thibodeau expect more of him this season. Gibson averaged 7.9 points, 5.2 rebounds, 1.3 blocks and 20.4 minutes last season.
"Thibs already told me he wants my role to change, be more of a leader now," Gibson said. "I worked out with him a lot during the summer. I worked out with him before the (Team) USA camp. He just wanted me to work out this whole year, build confidence and get better. He thinks I can do a lot more on and off the court. I'm ready to take that next step."
Gibson thought the next step was being more of an all-around player.
"Just playing more solid, just coming in knocking down some 15-footers, back-to-the-basket play, a lot of stuff like that I've been working on during the offseason, a lot of stuff like that in the USA camp," Gibson said.
Gibson is in the final year of his rookie contract. He said there have been talks about an extension, but either way he's not going to let it affect him.
"They're talking about that stuff now," Gibson said. "I'm not even thinking about that. A lot of people always talk about that all year long, all season long. I don't really worry about it. I won't really be thinking about it. I'm just going out there and playing my game."
Gibson admitted it will be an adjustment this season without "The Bench Mob." The Bulls lost Omer Asik, Kyle Korver, C.J. Watson and Ronnie Brewer this offseason and added Nazr Mohammed, Marquis Teague, Marco Belinelli, Vladimir Radmanovic and Kirk Hinrich.
"I was just with Ronnie in New York," Gibson said. "It's crazy to think he's a New York Knick now, C.J.'s a Brooklyn Net, Omer's in Houston, Kyle is in Atlanta. It was just so crazy because our bench was so talented. With so many valuable assets, we knew across the league a lot of teams would want these guys. It's sad, but things like that happen all the time."
Gibson recently returned to Chicago from California and planned to begin workouts at the Berto Center on Tuesday. He hoped to see a number of his teammates there as well.
"Right now we're just thinking about getting into training camp, that's why most guys are coming in right now," Gibson said. "We're going to have a quick head start on guys understanding the concept of the team. That's why I'm here a month early, so I can get down and dirty.
"The one thing about our team -- most of our core is still intact. This next step is going to be big for us because we're not going to have Derrick, and it's going to be a chance for guys to develop and mature. Not knowing when Derrick is going to come back, it's going to put a lot more pressure on guys to step up and perform. We understand that. We have guys who can play big-time minutes. Now it's up to us just to perform."