The ex-Red Devils captain, who won nearly every available club trophy, spoke about how Antonio co-hosts the BBC Sounds Footballer's Football podcast since 2021 along with Callum Wilson.
Keane told the Stick to Football podcast: I think that (podcasts) can be a distraction for a player, particularly if you're on the back of a defeat, and you're in the next day and everyone is having a bit of a laugh.
I don't think you should laugh for a week or two if you've been beaten."
Antonio responded on Sky Sports: It's dinosaur mentality because when he (Keane) was playing, every manager, every fan, everybody, constantly said, 'Focus on your football. Go to sleep with a football in your arms - the only thing you're allowed to think about is football. Your wife deals with your kids, don't play with your kids - football'.
That's what it was when he was playing. Obviously in time players who played with him went bankrupt because all they did think about was football and that's all it was.
Now, obviously footballers are focusing on their football, can do their football, but can also focus on other things: business, fashion, some are rappers now. People focus on other things.
If I've got time to do this then why shouldn't I? With the podcast I understand that if you've got battered on the weekend - which I did - it's not a thing about being sad for two weeks because there's another game coming next week. You're meant to forget what happened on the last weekend and make it better the next week.
That's why a lot of players struggle with mental health problems because people are telling them they're meant to struggle for two whole weeks because they got battered on the weekend.
No, you deal with it. You are sad when you leave and for that night."