Cole signed for $541,000 on Saturday, the same amount he made last year when he went 19-8 with a 2.60 ERA and finished fourth in National League Cy Young voting. His 2015 base salary was $531,000, and he earned $10,000 for making the All-Star team.
"When you perform at a level that draws the praise of management, teammates, coaches and fans, you expect appropriate compensation," Cole told the Pittsburgh Tribune-Review. "I understand the business of this game, but it is hard to accept that a year of performance success does not warrant an increase in pay."
Cole told the newspaper that club officials refused to go over $541,000 after making an original offer of $538,000, saying that was the most they could offer under the team's salary system for players who are not eligible for arbitration.
"They even threatened a salary reduction to the league minimum if I did not agree," Cole said.
Players with less than three years in the majors are obligated to accept the contract offered by the team, which can lower the offer if the player refuses to sign the deal. The major league minimum salary is $507,500.
Pirates general manager Neal Huntington said Sunday that the Pirates made a mistake when they were computing Cole's offer. The Pirates didn't account for Cole's All-Star bonus, he said.
As a result, the Pirates based their 2016 salary offer based on Cole's 2015 base salary without the $10,000 All-Star bonus he had earned. The Pirates then adjusted their offer based on the bonus, and Cole agreed to the deal.
Huntington said Cole "broke our scale" when it comes to making offers to pre-arbitration eligible players.
The GM said he understands Cole's unhappiness.
"We can empathize with him. At the same time there is a system in place that is negotiated by the union and by Major League Baseball," he told reporters.
Cole's $541,000 salary makes him the Pirates' highest-paid pre-arbitration player, Huntington told reporters.
Even so, Cole's agent, Scott Boras, was outspoken about his client's salary.
"What kind of message does that send to players?" Boras told the Tribune-Review. "The best deserve the best. You should reward the best. I can't believe that is a [owner] Bob Nutting-approved [salary] system. It doesn't ring with the conversations Bob and I had when Gerrit signed."
Boras told the newspaper that he would expect to get Cole a salary in excess of $650,000 if he were pitching for other teams, adding "I would think Bob would want to reward a guy for a special performance."
The 25-year-old Cole has been limited by inflammation around a right rib that he suffered during a training session last month. He returned to throwing off a mound Wednesday.
Cole received an $8 million signing bonus after being drafted first overall by the Pirates in 2011.
Information from The Associated Press contributed to this report.