Speaking on documentary "LeKBenzema," he revealed his irritation over the remark.
Mourinho told reporters: "If I can't hunt with a dog, I will hunt with a cat. With a dog you hunt more and you hunt better.
"But if you have not got a dog and you have got a cat, you hunt with a cat."
Benzema said it had been the cue for what had been "a good relationship" to begin showing strain.
He added: "After that, there were expressions and statements that were not necessarily well intended.
"I had the impression that it made him laugh. Even if he's someone I respect, after a while I started to lose it."
Benzema said he had an hour-long discussion with Mourinho in which he told him: "I'm a football player, you're my manager, I respect you, respect me as a player."
And he added: "From then on, there were no cats, no dogs or anything.
"I'm shy but if you make fun of me, I'll be straight. When you speak your mind, things are always better."