"A disrespectful fan threw a bag of peanuts at me,'' Jones said, according to USA Today. "I was called the N-word a handful of times tonight. Thanks. Pretty awesome.''
Jones, one of just 62 African-American players on the Opening Day rosters of the league's 30 teams this year, said he was the target of further taunts as the game continued.
Jones said he heard there were about 60 ejections in the ballpark Monday night; the Red Sox said that the number was closer to 30.
"I just go out and play baseball," Jones said. "It's unfortunate that people need to resort to those type of epithets to degrade another human being. I'm trying to make a living for myself and for my family."
Red Sox president Sam Kennedy issued an apology to Jones on Tuesday morning and said the team is looking into the incidents.
"The Red Sox want to publicly apologize to Adam Jones and the entire Orioles organization for what occurred at Fenway Park Monday night," Kennedy said. "No player should have an object thrown at him on the playing field, nor be subjected to any kind of racism at Fenway Park.
"The Red Sox have zero tolerance for such inexcusable behavior, and our entire organization and our fans are sickened by the conduct of an ignorant few. Such conduct should be reported immediately to Red Sox security, and any spectator behaving in this manner forfeits his/her right to remain in the ballpark, and may be subject to further action. Our review of last night's events is ongoing."
Massachusetts governor Charlie Baker and Boston mayor Marty Walsh also condemned the fans' behavior.
Fenway fans behavior at the #RedSox game last night was unacceptable & shameful. This is not what Massachusetts & Boston are about.
— Charlie Baker (@MassGovernor) May 2, 2017
Added Walsh in a statement: "This is unacceptable and not who we are as a city. These words and actions have no place in Fenway, Boston, or anywhere. We are better than this."
Jones said it was not the first time hecklers in the stands at Fenway had targeted him with a slew of racist abuse, but Jones told USA Today and The Boston Globe that Monday night's taunts were among the worst experiences of his 12-year big league career.
"It's unfortunate," he said. "The best thing about myself is that I continue to move on and still play the game hard. Let people be who they are. Let them show their true colors.''
Jones said the fan who threw the peanuts at him in the dugout was located and escorted out of the ballpark, which was confirmed to USA Today by Red Sox officials after the game. But Jones said a harsher punishment from the league should be given, such as a major fine or lifetime ban from the stadium. He called the actions of the culprit in question "pathetic."
"It's called a coward," Jones said. "What they need to do is that instead of kicking them out of the stadium, they need to fine them 10 grand, 20 grand, 30 grand. Something that really hurts somebody. Make them pay in full. And if they don't, take it out of their check.
"That's how you hurt somebody. You suspend them from the stadium, what does that mean? It's a slap on the wrist. That guy needs to be confronted, and he needs to pay for what he's done."
A five-time All-Star and four-time Gold Glove winner, Jones was the Orioles' 2016 Roberto Clemente Award nominee. The award recognizes a player "who best represents the game of baseball through extraordinary character, community involvement, philanthropy and positive contributions, both on and off the field," according to Major League Baseball.