Cardiff head to Burnley on Saturday and then face Brighton, who are five points above them, next Tuesday in a crunch stage of their season.
“We are running out of time and points,” Warnock said.
“We need 10 points, really, to have any chance whatsoever.”
Warnock has no doubt that his players are ready to fight for everything during a run-in that also includes clashes with Liverpool and Manchester United.
He added: “I’ve never seen anything other than a fighting spirit.
“I saw the desolation after the Chelsea game (in which Cardiff suffered a controversial 2-1 defeat), where we all felt we could have had more points on board. You can’t take that away.
LIVE ON talkSPORT
talkSPORT is your home of live football! Here's what's coming up on talkSPORT and talkSPORT 2…
- Slavia Prague vs Chelsea (Thursday, 8pm) – talkSPORT 2
- Southampton vs Wolves (Saturday, 3pm) – talkSPORT 2
- Manchester United vs West Ham (Saturday, 5:30pm) – talkSPORT
- Leeds vs Sheffield Wednesday (Saturday, 5:30pm) – talkSPORT 2
- Wigan vs Norwich (Sunday, 12pm) – talkSPORT 2
- Crystal Palace vs Manchester City (Sunday, 2:05pm) – talkSPORT
“The dressing room has not been like that this season, even when we have had poor results, but training has been good and they’ve really picked up. It’s been bubbly again.”
Warnock, meanwhile, underlined a sense of loyalty to the Cardiff fans that fuels an ambition to stay at the Welsh club next season.
“I just feel as long as Vincent (Cardiff owner Vincent Tan) wants me to stay, no matter what division we are in, I think I owe it to the fans to stay,” he said.
“I changed my mind in the last couple of months with the Emiliano (Sala) tragedy. It brought a lot home.