The Division I Committee on Infractions panel put Notre Dame on probation for a year and ordered a $5,000 fine, penalties the school agreed with. There were no bowl or scholarship punishments.
Kelly said he knew the vacated wins were a possibility since he and other Notre Dame officials met with the NCAA several months ago. He said he had hoped it would not come to that, saying he hoped "reasonable people would come to a reasonable decision."
"We did the right thing. I'm proud of our support staff, our academic support staff. I'm proud of the people that represented us here at Notre Dame during this time," Kelly said. "And if doing the right thing means that you've got to put an asterisk next to these games, that's fine with me. We still beat Oklahoma. We still beat Wake Forest, we still beat all those teams, so you can put an asterisk next to it. If that makes you feel better, then that's fine with me."
He said he doesn't believe he has any culpability in the case and has no reason to believe he won't be back as Notre Dame's coach next season.
"I think you guys are confusing this statement with the win-loss record," said Kelly, who is in the midst of his worst season at Notre Dame with a 4-7 record ahead of Saturday's game at No. 12 USC. "A win-loss record is always under scrutiny at Notre Dame, and it should be. That's part of it."
The report doesn't name the players involved, but stems from an investigation that began in August 2014 , when the university suspended defensive lineman Ishaq Williams, receiver DaVaris Daniels, linebacker Kendall Moore and cornerback KeiVarae Russell, who weren't allowed to play that season. The school later benched safety Eilar Hardy, who was allowed to return in midseason. Russell returned and played for the Irish last season.
According to the NCAA, the trainer was employed by the athletics department from fall 2009 through the spring of 2013 and "partially or wholly completed numerous academic assignments for football student-athletes in numerous courses" from 2011 into 2013. For the six players who got extra help, the trainer aided them in a total of 18 courses over two academic years. The NCAA also said the woman "continued to provide impermissible academic benefits to football student-athletes for a full year after she graduated" and was in her first year of law school elsewhere.
In all, the NCAA said, three athletes would up playing while ineligible, one during the 2012-13 season that ended with a blowout loss to the Crimson Tide in the national championship game and the other two the following season, when the Irish went 9-4.