The 25-year-old striker, who signed from Sunderland in January, said that the Bluebirds showed their battling qualities at the Cardiff City Stadium, which should stand them in good stead for their first Premier League campaign.
"It was very special, but the most special thing was getting the three points today," Campbell told Sky Sports News. "When you're a promoted side you don't want to wait too long to get points on the board so today was a massive bonus for us.
"The manager's been saying to us that we deserve to be in this league on merit. We did very well last season in the Championship and we've got to go out there and show everyone what we're about.
"We're going to be underdogs for a lot of the games this season but as we showed today we've got the determination and hopefully that will see us through."