Monteith, 31, died last Saturday of a heroin and alcohol overdose.
TMZ said the "Glee" star's mother Ann, brother Shaun and girlfriend Lea Michele viewed his body at the hospital where his body was taken, but his father Joe wasn't invited.
Joe, who is divorced from Ann, told the celebrity news website he is "totally devastated" he didn't get a chance to see his son's body and was only informed of his cremation after it happened.
"I always loved both my sons and am going to miss Cory very very much. I'm saddened at the fact that I couldn't have been there to see my son before he was cremated," Joe told TMZ.