The England defender has also stressed he did not mean to disrespect referee Mike Riley by turning his back on the official while he was trying to book him for the challenge on Wednesday night.
"I'd like to apologise to anyone I offended and of course Alan Hutton who I tackled," Cole said after watching both incidents on television this morning.
"I didn't mean to go in hard that way. It was high but I tried to read the ball and get the ball first, but he was a little bit too quick for me.
"It wasn't malicious and I'm a little disappointed with what people are saying, that I meant it.
"Of course it was a bad tackle at the time but in the heat of the moment you want to win the game and win every tackle, and as I said I'm sorry for Alan, but it was never meant."
Cole has been roundly criticised for his conduct towards Riley after the incident but the 27-year-old said everything happened in the heat of the moment and he did not intend to be discourteous.
But he accepted his behaviour was something he had to concentrate on keeping a grip on in the future.
"I'm an emotional person, things can happen on the pitch very quickly but I didn't mean to disrespect the referee," he added on Chelsea TV.
"I recognise this is a part of my game that I need to work on and control."