Alston said he left because he was upset that his teammates were lackadaisical after losing to the expansion Charlotte Bobcats on Friday night.
He apologized to his teammates Thursday after meeting with general manager Rob Babcock and coach Sam Mitchell.
"I expect not to be in the starting lineup," Alston said.
"I knew I made a mistake," he said. "I've made mistakes in the past and I've overcome those mistakes."
Milt Palacio has started in Alston's place at point guard and is expected to start Friday's game against Washington.
Alston has been in trouble before. During a loss to Boston on Dec. 3, Mitchell told Alston to get off the bench after he received a technical foul. Mitchell benched Alston for the rest of the game and didn't start him the next game. Alston was so upset, he threatened to leave the team and quit the NBA altogether before later backtracking.
Babcock says the team is trying to help Alston rein in his emotions. The Raptors signed the 28-year-old to a six-year contract worth between $27 million and $30 million this past summer.
"I think Sam is going to bring him along slowly," Babcock said. "He's not going to change over night. It's a long-term thing. We want to make sure we keep a handle on this and he keeps improving."
Alston was a second-round draft pick of the Milwaukee Bucks in 1998 out of Fresno State but spent his first season on the NBA's suspended list because of legal problems.
Alston's mother arrived in Toronto on Thursday.
"She told Rob she's bringing a belt, an extension cord and a hammer," Alston said. "If you don't see me sitting down on the bench you'll understand why."