After the game, Mourinho's anger spilled over to the car park as Tottenham were waiting to leave the stadium.
Posting on his Instagram account, Mourinho wrote: "Bad perfomances deserve bad results.
"Hope everyone in this bus is as upset as I am. Tomorow 11 AM training."
In response, Keown said: "In the dressing room surely? I'm not happy with it being so public.
"Maybe he didn't say anything [in the dressing room]. We hear that he didn't say anything and just walked out and left the players.
"I don't think my respect grows for the manager. Some of those players would have been wounded at half-time when they were taken off, the likes of Dele Alli.
"You feel it don't you - maybe my career is over at Spurs. But it's part of a collective, it can happen. I don't think the players that came on were any better."
Keown continued: "Well I'm not going to follow him but it's like, is this how we're going to communicate?
"If you want to talk to me, talk to my face. What are you doing posting stuff?
"When it was 3-3 against West Ham apparently he didn't speak to the players about it for four or five days but said an awful lot to the media.
"These are messages and I just think, keep it in house. It's a bit churlish, childish sometimes what you're hearing.
"Because players have to keep their mouth shut but he can say whatever he wants publicly. I'd rather keep it within the dressing room.
"If I'm not good enough I'll accept that. But I want to work hard to get back in the team, let's keep it healthy. I don't think that's healthy."