Fabregas arrived at Highbury as a teenager in 2003 and Kroenke revealed the decision to not stand in the former captain's way was down to the manager, as was Nasri's departure for Manchester City.
"That was between Arsene and him," the American told the Daily Telegraph. "I like the kid but I'm not going to change his mind.
"Arsene made the decision.
"If we wanted to be really hard about it, we could have done but Arsene believed that it was the right way to do it.
"I also get it on Nasri.
"If we didn't do something on Nasri people would be looking at us next summer and saying, 'Why didn't you do this?'
"We bought in a lot of resources that we can use on other players.
"I honestly didn't make the decision on Nasri.
"Of course the board talks about these things but at the end of the day, that's for Arsene."