"We're all disappointed. Sammy Lee has been a major part of this club for the past three years, but these decisions are made from upstairs and we just have to go along with it," said the midfielder. "I just hope they get the right manager in. I just hope the next manager can start working with us to get us out of this situation.
"It's important that we get a new manager in quickly, but it's more important that we get the right appointment.
"But I think the board and the chairman have more about them than that. They are more clever that that. They will know who the right manager is, what the right appointment is."
Nolan believes anyone who followed Sam Allardyce was always heading into one of the Premier League's "toughest jobs".
He said: "We have to realise that it was always going to be difficult to step into Sam Allardyce's shoes. It's probably the toughest job outside the top four.
"The success Sam had at Bolton, on a limited budget, makes it hard for anyone to follow. Sammy felt he could do it, but the board felt he could no longer do it.
"But we want to prove it's about us as well as Sam Allardyce.
"It's about this team and the new manager who comes in, proving everyone wrong and climbing up the table.
"It's about moving forward and we all believe that in the next five or six games we believe we can pick up points and move up the table very quickly."
Nolan added: "We just ask the fans to stick with us through this difficult time.
"If we stick together we can get ourselves out of it.
"We are working hard, we are doing our best and we know it's going to turn for us sooner rather than later."