The Reds fell to a 1-0 home defeat at the hands of Blackburn Rovers on Friday to find themselves just two points above the bottom three with four games to go.
Warburton told the Nottingham Post: "We are all in this together. I am not going to stand here and say 'they have to be better'. It is about all of us as players and staff. We have to win this fight together.
"We have to stand up and show our quality. I am not going to say we were unlucky, because we were not. We did not do enough. Now we have to make sure that we are good enough and that we do enough, starting at Cardiff.
"But it is about focusing on what we do. It is a fight now. We have a fight. The right result and the right performance today would have given us breathing space. But we are in a fight now. There is no doubt these players have the quality. You saw it last week and in other performances – they have the quality."
After Cardiff City away on Monday, Forest take on Reading, Queens Park Rangers and Ipswich Town to wrap up their season.