Jackson was awarded the team's $3.6 million offer rather than his $4 million request by Robert Herzog, Richard Bloch and Scott Buchheit, who heard the case a day earlier.
A 30-year-old right-hander, Jackson had surgery on April 13 to repair a torn ulnar collateral ligament.
No statistics or evidence from after March 1 are admissible other than contract and salary comparisons, timing that was set when Major League Baseball and the players' association agreed to the deal that ended the lockout.
Jackson had 18 saves in 2019 and had served as a top setup man the past two years. He was 2-2 with a career-best 1.98 ERA in 71 games in 2021, helping the Braves win their first World Series title since 1995. He had a 0.00 ERA in three Series games against Houston, allowing one hit in 3 2/3 innings.
He earned $1.9 million last year.
Teams have a 3-2 lead in decisions: Seattle second baseman/outfielder Adam Frazier ($8 million) and Kansas City outfielder Andrew Benintendi ($8.5 million) won and Atlanta third baseman Austin Riley ($3.95 million) and St. Louis outfielder Tyler O'Neill ($3.4 million) also lost.
Arbitration hearings usually are held during the first three weeks of February but were delayed by the lockout.
Hearings are scheduled through June 24. Players scheduled for hearings include Atlanta outfielder Adam Duvall, pitcher Max Fried and Dansby Swanson, along with New York Yankees outfielder Aaron Judge, New York Mets pitcher Chris Bassitt, Minnesota catcher Gary Sanchez and Philadelphia pitcher Zach Eflin.