However, he also claimed that there is "no way" that the defender will be sacked for the incident and added that Cole is in line to play at tonight's home match against Manchester United, BBC News reports.
Ancelotti said: "Obviously we are not happy with what happened but I have spoken with [Cole] - he was really disappointed, he said sorry, he made a mistake, it was an accident.
"Now obviously we are taking proper action but tomorrow he will play and I think he is in focus to play a good game."
He continued: "From outside nobody can say that here is out of control because we have internal discipline. We will take a decision. We don't want to speak outside with the decision we take here.
"It's not true that here there is no discipline. Because you can judge the player on the pitch. The players on the pitch are showing respect for the referee - they are showing respect for the fans."
Of suggestions that Cole could be sacked for the offence, Ancelotti said: "No there is no way for this. He is our player, he always had very good behaviour here. Now, we have to move on.
"Who didn't make a mistake in his life... The mistake was that the gun was here in Cobham. We didn't know the gun was here."
He added: "First, [Cole] said sorry to the guy that was involved in this, second sorry to the teammates, third sorry to the club."
> Police to investigate Ashley Cole shooting