A source familiar with the situation confirmed the fine.
The rule in question involved Bostic lowering his head and making forcible contact with a defenseless player's body, the source said. This wasn't a violation of the new "crown of the helmet rule," according to the source.
"I'm still trying to figure that stuff out," Bostic said. "Obviously I'm new to the league. There's going to be a lot of new things I'm going to have to find out. I'm learning from the older guys and really just finding out the process. I'm really just figuring out all of this stuff."
Bears' first-year head coach Marc Trestman said he thought it was a clean hit.
"I don't have any reaction right now about anything," Trestman said. "When I looked at it, other than to say that I thought it was a clean hit, his head was up and he hit with the shoulder from my vantage point on the field, and upstairs looking at it on the tape I thought it was a clean hit. That's all I need to say about it."
Bears starting weakside linebacker Lance Briggs tweeted about the fine Wednesday morning.
Shaking my head moment. Nfl fines jon bostic 21k for his clean hit against the chargers.— Lance Briggs (@LanceBriggs) August 21, 2013
Briggs went on to tweet, "Bostic's hit illegal. Hit on Dustin Keller. Legal."
"The league thought that (Bostic's hit) was an illegal hit; I disagree," Briggs said after practice. "I think that if you ask around the league, probably 100 percent of the league's going to say it was a legal hit, but it's not my call.
"You have to continue to play football the best way you know how and that's what he was doing. None of the referees seemed to think there was anything wrong with the play, guy coming in, first defense ... not my call."
Bostic hit Willie's chest region after a short pass during the Bears' 33-28 win Thursday. He separated the receiver from the ball, and the pass was ruled incomplete. Bostic was not flagged on the play.
"He could have allowed the receiver to run him over -- that's another technique," Briggs said when asked what Bostic could have done differently. "We could play the catch technique, we could take a charge ...
"All I saw on the play was receiver was coming in, full flow, defense coming out there, Bostic with a head's up play and not only did he make the hit, he jarred the ball loose."
The rookie out of Florida is scheduled to earn a $405,000 base salary in 2013 in addition to a $1,246,036 signing bonus, which means he's basically losing a game check. He can appeal the fine.
"Right now, I don't even know the whole process," Bostic said. "Like I said, I'm new to the NFL. This is my first year, so I don't know how this process exactly works. I've got to find out more about it and figure out exactly how everything is going to play out."
Bostic has been working as the Bears' No. 1 middle linebacker since veteran D.J. Williams suffered a calf injury at the beginning of training camp.
"I've just got to go out there, play football and have fun," he said. "That's the main thing. That's what I'm here for. I play football to have fun. These guys have been around all week. I'm excited to get back to work against new faces. I'm just trying to get that stuff to carry over.
"I'm always trying to get the ball back. Getting the ball back for the offense at that position on the field would have been big but we didn't get the fumble. But it is big. You want to get the ball back to the offense."
"I thought it was a clean hit, but I thought mine was a clean hit, too," Conte said. "That's not saying much. He'll appeal it and hopefully they'll reduce it. It's a lot for a rookie. He did get drafted in the second round, so he's got a little bit of money, but still, it's a tough thing, especially in preseason. But the best thing you can do is appeal it and hope it gets reduced."
ESPNChicago.com's Michael C. Wright contributed to this story.