Most likely he is referring to his own phone call to the wife of Jimmy Hoffa - Jo
Jo is terrified about the fate of her husband and Frank is trying to console her, knowing well that Jimmy is dead because
he has killed him a few hours before.
Frank is devastated by this phone call: he was not only involved in the death of his best friend but now also he has to lie to his wife. On top of that, this was the day when his daughter Peggy left his life, when she has realized what Frank has done.
So when later, slowly dying he says
What kind of man makes a... a phone call like that?
Frank admits that at that moment he became terrified of who he has became, that this single moment was the lowest point in his life.