"To me the whole thing is a giant nothing burger. Who cares? Even if they owned all of the streaming companies with all the features, it wouldn't make a difference to their income statement," he said in an interview on CNBC's "Squawk Alley."
The chairman of O'Leary Funds said that the music business as a whole is a "crappy" one and that Monday's announcements will do little to impact Apple's earnings this calendar year.
"Show me moves that protect and grow my dividend in Apple," he said. "This is not going to be material while I'm alive."
Steve Milunovich, UBS managing director and Apple analyst, said on Tuesday that services like Apple Music support device sales and shouldn't be looked at for the revenue they generate on their own.
"You can argue at this point that Apple Music is a bit defensive," he said in an interview on CNBC's "Squawk on the Street."
"But nevertheless they have to make up for the fact that the iTunes store is in decline, music has shifted elsewhere and now Apple is going there."
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Milunovich said he is more impressed with the integrated Apple ecosystem—different products in various categories—and that the company is more open to developers than it once was.
"Apple doesn't have to be first anymore, especially given their 400 million-plus user base of phones. I think what they did yesterday is probably sufficient."