Boston was swept in the first round of the playoffs by the Indiana Pacers, losing Game 4 Sunday.
The Celtics went 14-22 under Carroll to finish the regular season 10 games below .500, but they did eke out the last playoff berth in the Eastern Conference.
The playoff appearance was a mixed blessing for Boston and Ainge, who had said the team would be better off taking its chances in the draft lottery. Ainge did not attend the Celtics' first home playoff game Friday, choosing instead to take a scouting trip.
All-NBA first team
San Antonio Spurs forward Tim Duncan made the All-NBA first team Sunday, becoming just the sixth player to receive the honor in each of his first seven seasons.
Also on the first team were Los Angeles Lakers teammates Kobe Bryant and Shaquille O'Neal, Minnesota Timberwolves forward Kevin Garnett and New Jersey Nets guard Jason Kidd.
Garnett was the only player who was named on all 123 first-team ballots.
The forward set career highs with 24.2 points and 13.9 rebounds a game, helping the Timberwolves to the Western Conference's best regular-season record at 58-24.
Garnett also was the fifth player in NBA history to lead the league in both total points and total rebounds.
Duncan, a two-time MVP, was the only player this season who finished in the top 10 in points (23.3), rebounds (12.4), blocks (2.68) and field-goal percentage (.501).
The other players with seven straight All-NBA appearances to start their careers were Hall of Famers Elgin Baylor, Larry Bird, George Mikan, Bob Pettit and Oscar Robertson.
All-defensive first team
Indiana Pacers forward Ron Artest made the NBA's all-defensive first team for the first time in voting announced Monday.
Guards Kobe Bryant of the Los Angeles Lakers and Bruce Bowen of San Antonio, Detroit center Ben Wallace and Minnesota forward Kevin Garnett also were chosen.
Artest recently was the runaway choice for the defensive player of the year. He finished third in the league in steals (2.08 per game) and held the players he guarded to 8.1 points a game.
Wallace ranked second in rebounds (12.4) and blocks (3.04).
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