The Bluebirds took the lead twice against Liverpool on Saturday, but eventually succumbed to a 6-3 defeat at the Cardiff City Stadium.
Despite the result, Campbell has been left encouraged by his team's abilities as they reach their final seven games of the campaign.
"We are in a dogfight for survival and we are up for the challenge," Wales Online quotes Campbell as saying. "This will go to the wire and we know what we have to do.
"Over our last four matches we have played really well as a team. Nobody expected us to get anything against Liverpool, but we showed the spirit needed to climb the table."
Cardiff are currently second from bottom in the standings, three points adrift of safety.