Ole Gunnar Solskjaer's side sit second bottom in the English top flight and are three points adrift of safety following a crushing 4-0 home defeat to Hull City last Saturday.
Cardiff have won just five league games all season, with the appointment of Solskjaer as manager failing to inspire any sort of surge in form.
Since the former striker's arrival in January, Cardiff have won have won just once in the league, picking up four from a possible 24 points.
But Caulker, who signed from Tottenham in July, remains upbeat that they have the quality to survive.
"I have a lot of trust and faith in our players," Caulker told WalesOnline. "We have all made mistakes at times, but we keep together and encourage each other.
"It is now about keeping it tight and keeping as many clean sheets as possible. Our job is to show the character and spirit to bounce back.
"We will show our fight, our passion and go into every game believing in ourselves. The minute you stop doing that you are in danger of drifting away.
"With the manager behind us and the players we have there is no doubt in my mind we can still stay up.
"I felt confident from the start of this season we would stay in the Premier League and I feel the same way now.
"There are 11 games to go and Cardiff's fate is very much in our own hands.
"There is plenty of time to secure our future at the top level for next season. There's no need to start panicking and it wouldn't help if that happened.
"We've been through a transitional period since the turn of the year and the fans have been patient. I'd ask them to stick with us.
"It's clear, though, we have to start picking up points."
