The Bluebirds were looking to build on their miraculous draw with West Bromwich Albion but fell to a 3-0 defeat at Cardiff City Stadium, which leaves them six points adrift of safety with just five games remaining.
Caulker told the Daily Star: "It's difficult to explain it. I don't know what went wrong. It was not for the lack of trying because the boys ran their socks off. But we are going to have to dig deep and show a lot more fight and passion.
"We apologise to the fans that turned up and gave us great support as always. We were very disappointed with it. We know we can perform a lot better than that.
"We've given ourselves a mountain to climb now. It's going to be five cup finals between now and the end of the season."
Cardiff are 19th in the Premier League with 26 points after 33 games.