Jenks acknowledged that his pitch in the 3-2 win was intentional but that he won't do it again.
Asked if the ninth-inning pitch that came with two outs "got away from him," Jenks said emphatically that he threw the pitch with a purpose, after Rangers starter Kevin Millwood had hit Chris Getz and Carlos Quentin with pitches earlier.
"No, I meant to. To send a message," Jenks said, according to the Chicago Tribune. "Basically I was saying, 'I'm sick of seeing our guys get hit and hurt and almost get taken out of the game.' I threw it with intention."
Kinsler popped out to second to end the game after home plate umpire Lance Barksdale issued warnings to both teams.
Jenks added his intent wasn't to hit Kinsler.
"I'm not going to put a guy on in that situation," he said, according to the Tribune. "I was not going to hit him. I made my point with that pitch and it came across the way I wanted it to.
"I'm not going to go dirty. I was going to keep it low and behind him."
White Sox manager Ozzie Guillen said Jenks' pitch behind Kinsler wasn't as a result of a bench order, and that he thought Millwood's pitches that hit Getz and Quentin weren't intentional.
"That's his problem," Guillen said of Jenks, according to the Tribune. "I know what I see and what I think. I don't think it was the right moment to do it because we can get in trouble. But if he says he did it, I respect his word and I can't do anything about it right now."
Jenks said he hadn't heard from MLB. He said his wife called him after hearing that the league will look into the incident.
Since Guillen became manager prior to the 2004 season, White Sox pitchers have hit 270 batters, the lowest number in baseball. White Sox batters have been hit 331 times during that same span.
"I see a lot of my hitters almost get broken hands on back-to-back days," Guillen said. "I never retaliated, because in my opinion, it wasn't on purpose. But if I'm a hitter and I keep getting hit, and my pitchers don't protect me, I don't want to play for them. That's the way baseball is and that's the way baseball is going to be."
Information from The Associated Press was used in this report.