The union said in its own statement that it "strongly disagrees" with the ruling but added "we recognize that a final and binding decision has been reached.
"We respect the collectively-bargained arbitration process which led to the decision," the union said added.
Rodriguez, however, plans to continue the fight.
"This injustice is MLB's first step toward abolishing guaranteed contracts in the 2016 bargaining round, instituting lifetime bans for single violations of drug policy, and further insulating its corrupt investigative program from any variety defense by accused players, or any variety of objective review," he said.
"I have been clear that I did not use performance-enhancing substances as alleged in the notice of discipline, or violate the Basic Agreement or the Joint Drug Agreement in any manner, and in order to prove it I will take this fight to federal court. I am confident that when a federal judge reviews the entirety of the record, the hearsay testimony of a criminal whose own records demonstrate that he dealt drugs to minors, and the lack of credible evidence put forth by MLB, that the judge will find that the panel blatantly disregarded the law and facts, and will overturn the suspension."
Rodriguez has claimed Selig was on a vendetta to smear him as a way of burnishing the commissioner's image following the Steroids Era. Both sides have admitted paying for evidence as they prepared for the hearing.
Fourteen players were penalized following the Biogenesis probe, and they all accepted penalties. Milwaukee outfielder Ryan Braun sat out the final 65 games of the season, the other players were given 50-game suspensions.
A-Rod's drug penalty was for "his use and possession of numerous forms of prohibited performance-enhancing substances, including testosterone and human growth hormone over the course of multiple years," MLB said last summer. His punishment under the labor contract was "for attempting to cover up his violations of the program by engaging in a course of conduct intended to obstruct and frustrate the office of the commissioner's investigation."