Enzo has been suspended by Chelsea for two games, including today's clash with Manchester City, for discussing publicly multiple times about eventually leaving for Spain and potentially Real Madrid.
However, while the Argentina midfielder has copped the internal ban, Marc Cucurella and Moises Caicedo have avoided punishment despite saying similar things in recent weeks.
Poyet told Tribalfootball.com: " I didn't like it as a football player and I didn't like it as a coach. I didn't.
"They could have just kept him out if that was their decision (rather than making it public). I hope that Enzo takes this situation in the right way that he somehow calms down and looks to the future.
"There's two things why I didn't like it: the interview was in Spanish. It was not only one. There were three different ones. I know what he said and what he meant. I saw Cucurella's in Spain, and I saw one from Caicedo as well.
"And if you understand Spanish and you understand the football player, there is no big difference between the three of them. Now, you can understand one way. I can understand another. I understand my way. I don't care about the other way. And why only Enzo is interesting..."
Poyet also considered: "There is something there that we don't know. And then, obviously, the agent getting involved and everybody else. But why is it so important the personality and the reaction of Enzo? Because we are all different. And some people will react in one way.
"Some people will react in a different way. And he is a hundred million dollar player. But you've listened to the interview.
"Now, he said he would like to live in Madrid. I would like to live in Los Angeles, in L.A! I don't know. Oh, no, he wants to work in Los Angeles Galaxy...?! Well, you know. Now, it was something inside that we don't know about..."
- Gus Poyet was speaking to Tribalfootball on behalf of William Hill