The former Manchester United man believes that Cardiff can take inspiration from the other two sides who were promoted last year.
"We all watch [football] because we believe something special is going to happen," Campbell told The Mirror. "Hopefully we can be part of that miracle this year and survive.
"When [Crystal] Palace came up from the Championship with us and Hull [City], everyone expected all three of us to go back down. With their new manager, Palace have improved massively. They are nowhere near the relegation zone.
"Hull too have had a brilliant season and are in the FA Cup final, so we can take inspiration from that."
Cardiff's next game is against Stoke City on Saturday afternoon.