He 'offered no apology for' his bad behavior. [=he didn't say he was sorry for acting badly]
The company issued/delivered an official 'apology' to its customers for its error.
He's a poor/sad 'apology for' a father. [=he's a bad father]
(..) I am, Mammy. I am. "Oh, she wept with delight when he gave her a smile "And trembled with fear at his frown." Hello. I'd like to extend my apologies for my conduct of last night. Oh, but Rhett.... I was very drunk... ...and quite swept off my feet by your charms. (..)1939 Gone with the Wind
(..) and arrogance. -That's Yankee treachery! -Sir, I refuse to listen to any renegade talk! I'm sorry if the truth offends you. Apologies aren't enough, sir! I hear you were turned out of West Point, Mr. Rhett Butler... ...and you aren't received by any decent family in Charleston, not even your own! (..)1939 Gone with the Wind