Aaron Hernandez's lawyer, Jose Baez, is adamant the ex-NFL star is "not a killer" -- and says the jury in his double murder case GOT IT RIGHT with the not guilty verdict. 

Baez says there was "an abundance" of reasonable doubt in the case -- and tells us he's very happy for Aaron and his family now that the former New England Patriots tight end has been exonerated.

So, what's next for Hernandez? Baez says he'll start taking a look at Aaron's other murder case in the hopes of overturning the conviction.