City have picked up only one point from their last four league games to slip to 19th place and three points adrift of safety.
After losing 4-0 at home to Hull City, they produced an improved performance in a 1-0 defeat at Tottenham last week and centre-back Caulker believes they can build on that as they prepare to take on bottom-of-the-table Fulham in a crucial match at the Cardiff City Stadium.
Caulker told Sky Sports News: "It's a vitally important game for both teams and we are both desperate for the points.
"We've set ourselves the target of getting five wins from the next 10 games. Of course it's going to be a big ask, but we are due a run, we haven't won back-to-back games all season.
"We are looking to put three or four wins together and hopefully remain in the Premier League.
"It was a much better performance at Tottenham. We changed our formation around and I think that allowed us to be more solid and try to counter-attack.
"There are a lot of positives to take from that game. It was a challenge as we had only trained four or five days on that shape. But the boys coped well with it and we were a lot harder to beat.
"There's a lot of fight back in the camp and a lot more belief, which is important.
"Hopefully now with the home game against Fulham, we can get the crowd behind us and put on a performance and come back with three points."
Caulker was called up to the England squad for the friendly against Denmark in midweek after Phil Jagielka was injured but he appears unlikely to make the World Cup squad at this stage.
England boss Roy Hodgson said after the Wembley game that he had his four centre-backs for Brazil - Jagielka, Gary Cahill, Chris Smalling and Phil Jones - but Caulker has not given up hope yet.
He said: "It all depends because there are always injuries floating about so, if it was to happen to one of them, then it could be me he calls on.
"The main thing is for me is to keep up my form for the club, keep Cardiff in the Premier League and you never know what could happen in the summer."