Brown, who had been listed as questionable on Tuesday afternoon, said he had "some mild symptoms for the most part," including some breathing issues that he used meditation to navigate through.
"The most concerning was my breathing," Brown said. "I had to really focus to get my breathing kind of back to normal. ... But the more I focused on it, the better I was able to gain more efficiency in it."
Brown said the Celtics have provided an inhaler for him to use if he needs it, but he hopes it won't be necessary Wednesday night (TV: ESPN, 7:30 p.m. ET).
"I feel pretty good for the most part," Brown said. "Just coming off being in quarantine and ramping the intensity level, there's obviously concerns, risk of injury and things like that. Some of the coaches are concerned it might be too soon, just because this is the NBA."
Center Al Horford, who also tested positive for COVID-19, and Josh Richardson (migraine) will be out for Wednesday's game. Udoka gave no timeline for Horford's return other than he was doing well physically and that Grant Williams would start alongside Tatum, Brown, Marcus Smart and Robert Williams.
While former teammate Kemba Walker will be on the opposing side for the Knicks, Brown said he and Jayson Tatum are ready to take on the challenge of leading the franchise back to the top of the Eastern Conference.
"Absolutely," Brown said. "It puts a smile on my face. I've never been somebody to back down from a challenge in my entire life, [as] my mom would tell you. And Jayson carries that same energy.
"So we might not be screaming from the mountaintops, but we absolutely appreciate and are grateful to be in that position, and are excited to navigate being in this position, taking it head on."
It was an offseason of change in Boston. Danny Ainge, the team's longtime president of basketball operations, stepped down from his job and was replaced by Brad Stevens, the team's longtime coach. In the following few weeks, Stevens traded Walker in a deal that brought back Horford, and he hired Udoka to be the new coach.
All of those moves were predicated around building the franchise around Brown and Tatum, the team's star wing tandem that, the Celtics would argue, rivals any pairing in the league.
Brown said he's excited to see how he and his teammates can navigate the opening weeks of the season.
"How we handle adversity -- I'm looking forward to those moments," Brown said. "Because obviously Celtics fans, writers and media want us to come out and just dominate and be the best team of all time. But we've still got some things to work on and work through, and I'm excited to navigate winds -- to be a voice in guys' ears because I've seen it, I've been through it. To continue to persevere, to be positive.
"It's a long season, man. We've just got to play the games regardless of what the hype is on paper or what people are talking about. We'll just focus on coming in every day, doing your job, setting our instincts on defense and let things kind of fall from there."
Brown expressed appreciation for the time he spent with Walker in Boston, and said he learned a lot from watching Walker's pick-and-roll "wizardry."
Brown also pushed back when asked why things "didn't work" with the Celtics and Walker, who was traded just two years after signing a max contract as a free agent.
"I think that's subjective," Brown said. "I think it did work. Injuries had a lot to do with it. We went to the Eastern Conference finals with Kemba, a couple of games away from going to the Finals, couple of plays away from going to the Finals.
"... So that's subjective. I think it did work, I think we did mesh, and while I think we didn't necessarily achieve what we wanted to, I don't think that's on him. I don't think it was because of him. I really don't."
As for Udoka, the new coach said he didn't have any particular emotions about his first official NBA game. He said he slept fine Tuesday night, and that this is a lot simpler than playing in games was.
"I think maybe to my staff, they're probably surprised or whatever, but it is what it is," Udoka said with a laugh. "I guess my playing career and I've been through a lot as a player, was way harder than this. So that kind of prepared me for it. But being in Philly and Brooklyn [as an assistant coach] the last few years, I think it's prepared me for a lot of different situations, and so that's just been always been my mindset anyway."