Cole will be fined for breaching club discipline and Zola said: "We are professional sports players and we have to look after ourselves and look after our bodies.
"During the week our training sessions are very demanding so they can't afford to go out and stay late. For me that is a very important matter. I am not going to close an eye on things like that. The players know that already.
"I used to go early to bed and wake up very early but that was my rhythm. Everybody has got their own rhythm.
"I am not saying everybody has to go to bed at 11pm but it has to be reasonable. This time was too late.
"The players have to realise that if they want a clear mind and a fresh body in training they have to have at least eight hours sleep."
Critics claimed Zola could be too nice to be a top flight manager - but his decision to crack down on Cole's indiscretion gives him the chance to prove otherwise.
"Being nice doesn't mean that I am stupid," he said.
"I have a responsibility and I will take it seriously. I have to take decisions. I have to look after a balance here and if somebody makes a mistake I am ready to be the one who forces people to do things in the right way.
"When I was at Chelsea, not everything was perfect. Some players made mistakes and they paid for it.
"Every now and then you can make a mistake, it is normal, but as long as it doesn't become a habit because you are spoiling your chances and your team's chances.
"I am 100% certain Carlton Cole realised this."