Cotterill was officially unveiled as the new Forest manager at a press conference on Monday, having been announced as Steve McClaren's successor at the City Ground before the weekend after a compensation package was agreed with Portsmouth.
The 47-year-old walked out on Pompey on Friday afternoon after a turbulent 16 months at the south coast club.
Cotterill admitted is was a difficult decision to leave but conceded he could not turn down the opportunity to take charge at Forest.
"Maybe there is more stability here," he said. "It was unique what happened there. I went through a few owners there. It was three if you include the administrator. We went through a lot together down there over the past 16 months and it was very, very difficult to leave.
"But you do not get many opportunities in life when it comes to managing Nottingham Forest. The fans were fantastic with me at Portsmouth but this kind of chance does not come along very often.
"Leaving the dressing room was tough, given the relationship I had with my staff. We were a big family and I have never been through anything like what we went through there. I don't think any manager in football has."
Cotterill, meanwhile, insists he is not daunted by the challenge of bringing success to Forest on a shoestring budget - because he has done it throughout his managerial career.
The new Reds boss has been told he must wheel and deal in the transfer market, moving players out at the City Ground before he can bring new ones in.
"I never had any money at Cheltenham, Burnley or when I was over the river at Notts County, and people know what I had at Portsmouth," said Cotterill. "I seem to have done okay with that, so this situation does not hold any fears for me.
"We have to try to maybe improve the squad - whatever that means because I don't quite know yet. Whether that is trading or whether it is working on the training pitch, I don't know yet. But I am okay with that, really. I am comfortable with the situation.
"What is certain is that I will be stronger for having come through that experience at Portsmouth. I am a better manager now than I was when I walked through the doors there."
David McGoldrick has returned from his month-long loan spell at Sheffield Wednesday and Cotterill has the option of including the striker in the squad for his first game in charge against Middlesbrough on Tuesday night.