Ware was down after being hit by safety Nicco Fertitta, resulting in a targeting penalty and Fertitta's ejection. Officials saw only the second incident, which came in the fourth quarter, and flagged Tillery for unsportsmanlike conduct.
USC offensive tackle Chad Wheelerconfronted Tillery after the incident with Ware.
"I just saw an injured, vulnerable player. That could've made it 10 times worse if it had some oomph to it," Wheeler said, according to the Los Angeles Times.
Banner summed up the Trojans' feelings with a reference to Tillery's jersey: "[No.] 99 is dirty."
Video and GIFs of Tillery's actions immediately went viral.
"I did not [see the plays]," Kelly said. "I know he got a personal foul penalty, and I subsequently took him out of the game. I had a conversation with him. Any time a player has a personal foul penalty, I pull them out and have a conversation with them. I did that with Jerry, but I did not see [the plays].
"Accountability is built within any program. Jerry has to be accountable for his actions every single day. Jerry is a good kid, and if he made a mistake we'll hold him accountable for that mistake. We'll take a look at it."
Tillery was not made available to the media after Notre Dame's 45-27 loss to USC, which wrapped up the Fighting Irish's season at 4-8.
"You just can't do stupid things like that," Notre Dame defensive lineman Jarron Jones said. "That's going to reflect on you as a player. That's going to reflect on your character."
ESPN's Arash Markazi and The Associated Press contributed to this report.