Hiddink, Chelsea's temporary manager until the end of the season, told a news conference at Chelsea's training ground on Friday that he had disciplined the 28-year-old England defender following his arrest.
Photographs of Cole handcuffed by police outside The Collection bar in South Kensington, London, were published on Friday.
Cole however, has been included in the squad for Chelsea's FA Cup quarter-final against Coventry City on Saturday. He missed training on Thursday after being released from a police cell at 5.37am and was handed an 80 pounds fine for abusing police officers at 2.15am.
The maximum he can be fined by Chelsea for indiscipline is two weeks' wages, which was widely reported to be around 160,000 pounds by British media on Friday.
Hiddink said he would not tolerate such irresponsible behaviour again and also said that he had spoken to skipper John Terry and young defender Michael Mancienne who were out with Cole on Wednesday night.
The 62-year-old Dutch coach said: "Ashley went too far and I am a strict disciplinarian, I tackled him on his behaviour.
"I talked with Ashley this morning about the situation and he has publically apologised about his conduct and his behaviour to the police officer. It is a private matter and we have internally disciplined him, too.
"I have spoken firmly with him about his responsibility. There are rules inside the club regarding going out. So I had a firm talk with him and the rest of the group. What is normal and good in this is that he apologised for his abusive behaviour."
Hiddink added: "We have to close the case. That is why I tried to continue with the other daily routine as we have an FA Cup game tomorrow. I spoke to him firmly and the captain. But we have to put it in the right perspective."
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