Cundy insists Cucurella should be suspended by Chelsea just like Enzo Fernandez for talking publicly about the prospect of leaving the club.
Cundy told talkSPORT: "From a personal point of view, and I said it at the time, keep your mouth shut, that applied to both of them.
"I, personally, would have also done the same to Cucurella. I think, to punish... Enzo's was flirting with Madrid. I don't want to go over old ground but, that was his decision until it went public. I think Cucurella's comments as well, not helpful, keep your mouth shut.
"You're paid to play football, get on with your job, you're not a politician. Do your job better on the pitch, that's where I would come from.
"I felt something had to happen, I think there had to be a public display of, 'This is not on, this is unacceptable. You're paid by this football club, you work for this football club to go and play football, and to the best of your ability'.
"Well, I think it's fair to say neither of those, and they're not the only two by the way, have not done that. But they're the two that chose to speak in public.
"I don't know what, as a football club, you're supposed to do, if you're Rosenior or the hierarchy, you've got to be seen to do something, you can't let players get away with that."