Despite the loss, Rodriguez tied the record for the highest salary in an arbitration decision, a mark he shares with Alfonso Soriano, who lost his case against Washington in 2006, and Ryan Howard. Howard beat Philadelphia on Thursday.
The decision on Rodriguez was made by arbitrators Stephen Goldberg, Elizabeth Neumeier and Steven Wolf, who heard arguments Thursday in St. Petersburg, Fla.
Rodriguez made $7.1 million last year, when he tied for second in the AL with 40 saves. He is eligible for free agency after this season.
Owners won six of eight cases that went to hearings this year.
Tony Reagins, who replaced the retiring Bill Stoneman as the Angels' general manager in October, said the arbitration hearing was "interesting."
"Obviously, we knew what our case was going in, and it was interesting to see the other side, their perceptions," Reagins said Friday morning before the outcome was announced.
"You hope that when the decision is made, you can resume work, understanding that this is a part of the business
- not a fun part of the business, but something you go through," he said. "At the end of the day, hopefully we can focus on baseball and put this behind us."
Rodriguez recently expressed dissatisfaction that the Angels have not signed him to a long-term contract, and indicated he might leave as a free agent after this season. Although the club has offered him a longer deal several times in the past, he has opted to sign for one year each time.
Its top offer was believed to be around $34 million for three years.