The incident occurred following the Warriors' 106-98 win over the Clippers on Sunday at Oracle Arena.
Jones said he would appeal the fine and stood by his explanation Sunday that the bump was not intentional and he was simply trying to walk off the court.
"Some people like to draw attention to themselves and make themselves bigger than what they are," Jones said. "I think it was more him trying to draw attention to himself and wanting to be the reason why somebody else got fined. It is what it is."
Green did not take kindly to the bump and told reporters as much in the locker room.
"I think he wanted a reaction from me, but he don't play," Green said, noting that Jones is averaging a career-low 4.6 minutes per game this season.
Clippers coach Doc Rivers said he didn't see the incident until he arrived at Staples Center before Monday's game against the Minnesota Timberwolves.
"Wow, that was such a violent bump," Rivers said sarcastically. "It was amazing. I told Dahntay, 'You have to be careful; that was too hard.' I guess that tough guy in Golden State, that bump was too hard for him, clearly the way he reacted, my goodness. I thought that guy was tough."
Green explained his lack of reaction Sunday, saying, "Me getting suspended and him getting suspended, it's different."
He added, "If [Jones] gets suspended, they may not even notice."
Jones said he doesn't know Green and was taken aback by the personal nature of his postgame comments.
"I was surprised because that was a little bit immature," Jones said. "He wanted to make something of it."
Jones smiled and laughed as he answered questions about the incident.
"I thought it was just a brush, honestly and truthfully," Jones said. "I may be stronger than what I think I am. I didn't do it on purpose. I don't have a reason to do it on purpose. It's cool. I apologize if I hurt his feelings."
Green had said the bump should warrant scrutiny, saying, "I definitely expect that to be reviewed by the NBA. For him to look at me, look at me again, and bump me when I'm doing a postgame interview -- that's really smart, too, when it's on ABC. The postgame interview is the highlight of that segment and you bump somebody."
Green wasn't finished with Jones. In explaining the shooting guard's behavior, he said: "He got some camera time, which he needed because there wasn't much celebration from their bench today, so you didn't see him much. He got the camera time he was looking for."
ESPN.com's Ethan Sherwood Strauss contributed to this report.