Former Louisville basketball star Kevin Ware is standing up for Rick Pitino amid his suspected involvement in the NCAA recruiting sting ... saying his ex-coach is being unfairly fingered by the feds.

"What are you doing a full FBI investigation on? ... That don't make a lot of sense to me unless you were already digging, trying to make Rick to be that culprit and take that fall," Ware told TMZ Sports.

Kevin says he didn't notice anything fishy when he was playing for the Cardinals from 2011-2014 ... including any sign of Katina Powell -- the escort whose prostitution scandal rocked the university last year.