Owen's social media reply comes after a story involving he and Real Madrid striker Karim Benzema went viral over the weekend.
The 29-year-old was referring to when Mourinho described his options up front at the Santiago Bernabéu to be like going hunting with a cat, rather than a dog - a flamboyant way of saying beggars can't be choosers.
"But if you have not got a dog and you have got a cat, you hunt with a cat".
"Ferguson said that he wanted to sign Benzema and that I could only sign for Manchester United if he did not, which is what happened", Owen said in an interview with Canal Plus. With a dog you hunt more and you hunt better.
"I am grateful to Benzema for signing for Real Madrid as if not then I would not have played for Manchester United". "I thought those comments made him laugh and even though there was respect, I started to become irritated".
Benzema admitted he met Mourinho for a one-on-one discussion in which he said: "I'm a football player, you're my manager, I respect you, respect me as a player".
"It's always better to speak your mind and I'm usually quiet but if I'm annoyed, I will say so".
Los Blancos are now eight points behind Barcelona at the top of the league table, with Valencia also four points ahead of Real Madrid this season.