Major League Baseball imposed the penalty Tuesday. It did not disclose the amount, however a source told ESPNChicago.com that Jenks was fined $750.
"What's done is done," Jenks said. "Hopefully after today, we can get by this and go play some baseball."
Jenks sailed a fastball in back of Kinsler on Saturday. Jenks later said the pitch was intentional because he was tired of watching White Sox batters getting hit with no retaliation.
White Sox manager Ozzie Guillen was relieved his closer avoided a suspension.
"I was pleased. The way baseball is going right now, they're severe about fines and suspending people," Guillen said. "I think they did what they're supposed to do. Hopefully we won't have to deal with this any longer."
Since Guillen became manager prior to the 2004 season, White Sox pitchers have hit 271 batters, the lowest number in baseball. White Sox batters have been hit 331 times during that same span.
As for Jenks, he won't say what he'll do if the same situation presents itself again.
"We'll have to see," he said.
Rangers manager Ron Washington refused to be drawn into the hit-by-pitch debate.
"I have no reaction to that," Washington said. "We don't play the White Sox anymore. They can think all they want. I told them we didn't throw at anybody."
Washington said the umpires never warned Texas pitchers about throwing at Chicago hitters in any of the six games.
"Because there was nothing going on," Washington said. "I don't care how the White Sox reacted."
As for Jenks admitting he was getting even, Washington said, "[if] my guys get hit six times and somebody thinks they've got to take care of business, take care of business, don't talk about it."
Information from The Associated Press was used in this report.