Jenks, who signed a two-year deal with Boston last week, expressed disappointment to MLB.com that the White Sox decided not to re-sign him. He told the website he was "looking forward to playing for a manager who knows how to run a bullpen."
Oney Guillen called Jenks an ungrateful "punk" in a series of Twitter posts. In one, he wrote that Jenks should "be a man and tell the manager or the coaching staff how u feel or the organization when u were with the sox not when u leave." In another, he wrote that Jenks "cried in the managers office bc u have problems now u go and talk bad about the sox after they protected u for 7 years ungrateful."
Oney Guillen resigned from his job in the scouting department in March after the organization took exception to some of his tweets. He previously posted critical comments of White Sox general manager Ken Williams.
Jenks, whose 173 career saves are second all-time in White Sox history, also expressed frustration with Guillen's offseason comments that Jenks would have to earn the closer job if he returned to Chicago.
"With the way Ozzie was talking this winter and the way he treated me, I don't want to fight with the guy," Jenks told MLB.com. "How many times did he question my ability, and then saying how he would love to have me back, but I would have to come to spring training and fight for the closer's role like anyone else?
"Why would I come back to that negativity? I'm looking forward to playing for a manager who knows how to run a bullpen."
White Sox pitching coach Don Cooper said he was disappointed by Jenks' comments.
"There's a right way and a wrong way to handle things, and I think Bobby handled it the wrong way with his comments, simple as that," Cooper said Wednesday on "The Afternoon Saloon" on ESPN 1000. "I think he's talking out of frustration. He got himself a nice contract. You should move on, be a professional and just leave everything lie. Don't burn any bridges.
"Bobby has been hailed by us since 2005. We've done Bobby a service, and Bobby has done a service back for the organization. Too many things have gone on for it to end that way. He chose a poor way to end it."
Officially, the White Sox distanced themselves from Oney Guillen's latest comments, saying he is "not a member of the White Sox organization, and in no way does he speak for the Chicago White Sox."
Information from The Associated Press was used in this report.