The Welsh club look destined to make a quickfire Championship return, with their plight underlined by a 3-0 home defeat to Crystal Palace last Saturday.
It left them six points from safety with just five games left - Southampton, Sunderland and Newcastle away, while Stoke and Chelsea are their remaining opponents at home.
"Staying in the Premier League is all the motivation we need. There is no other," Cardiff captain Caulker said.
"We have to show more fight than we did against Palace. We have to draw confidence now from those games we've had this season where we have played well.
"We are going to have to find some form and a little bit of luck along the way, too. That would not go amiss.
"We've got some tough, tough games coming up now. We can't deny that. We do have a mountain to climb."
Cardiff's recent form does not suggest they will realistically climb out of the bottom three.
They have posted one win in the last nine league games and conceded 15 goals across their past five fixtures, including six at home to Liverpool.
"We do need to win at Southampton," Caulker added.
"Everyone wrote us off in the opening home game of the season against Manchester City, and we proved them otherwise and went and won the game.
"We've got belief we can stay up. We need to put in a performance and get a result at Southampton now.
"They have been very impressive in the Premier League and they are going to be a very hard team to beat, but we are going to have to beat them if we want to stay up."
Cardiff boss Ole Gunnar Solskjaer struggled to contain his anger after the Palace loss, which proved arguably their worst performance since he succeeded Malky Mackay as manager in January.
Solskjaer said he is looking for players with "belief, leadership and loyalty" for the Premier League run-in, and strongly hinted there will be changes for the trip to St Mary's.
England international Caulker added: "Credit to Palace, they came out strong. But at home with the crowd behind us, we want to perform better than that.
"Palace were very direct and they hit us with three sloppy goals from our point of view.
"They will be delighted, but we have to fix things up and be better defensively. We've leaked a lot of goals of late."