Jackson's letter was e-mailed to season ticket-holders and posted on the Bobcats' website hours before he was to play against the New Jersey Nets in his first game since his punishment.
Jackson, who has become the face of the NBA's crackdown on bad behavior this season, said he let his teammates and coaches down, "but more importantly, I let our fans down."
"In my heart, I know I have to adjust my emotions on the floor and I vow to work harder than ever to not put myself or this team in that situation again," Jackson wrote.
Jackson was suspended without pay after his first-quarter ejection Saturday against the Milwaukee Bucks for verbal abuse of referee Eli Roe and failing to leave the court in a timely manner. Jackson missed Wednesday's loss to the New Orleans Hornets.
Last month, he was fined $50,000 for verbal abuse of the officials after a loss to the Detroit Pistons in which he was assessed a technical foul by referee Steve Javie.
Before the season, the NBA sent out a video to teams showing behavior toward referees that would no longer be tolerated. One of the first clips was Jackson flailing his arms and running after an official.
The new regulations have been tough on Jackson, whose six technical fouls are tied for the league lead. That doesn't include one technical that was later rescinded by the league.
"I understand the rules that the NBA has established to govern players' behavior on the floor and I respect the job the officials have each night," Jackson wrote. "NBA players are bigger, faster and more athletic than ever, so being able to call a perfect game each night and see every foul is tough, and I have to take that into consideration."
Jackson has a history of volatile behavior. He served a long suspension for his role in the infamous Indiana Pacers-Pistons brawl in 2004. He has clashed with coaches and in 2009 served a one-game suspension while playing for the Golden State Warriors for getting his 16th technical foul of the season.
Jackson was traded to Charlotte early last season and helped the Bobcats reach the playoffs for the first time. He's averaging a team-high 18.1 points this season.
"As a co-captain, I have to lead by example and I feel it's my obligation and commitment to this team to carry out those responsibilities," Jackson wrote. "I hope to continue bringing you memorable moments on the court and not for my behavior."
Bobcats coach Larry Brown said he thought Jackson's letter was sincere but also wondered how much he'll be able to rein in his emotions.
"He's a lot like Rasheed [Wallace]. When he thinks things aren't fair, and Allen [Iverson] was the same way, they get frustrated by it," Brown said. "Some guys can fight through that. I think sometimes they win with jack.
"But from my perspective, when a guy gets upset when they think things are unfair, he shows me he cares. That's more important for me," Brown said.