The 25-year-old striker signed for the Welsh club in January, but knows exactly what it takes to mix it in the top flight having featured for Manchester United, Tottenham and Sunderland so far during his career.
But after losing 3-2 to Brentford and drawing 1-1 with Cheltenham Town in pre-season, the forward believes they need to step up their game if they are to be competitive on their return to the top table of English football after 51 years.
"The mistakes we have been making during pre-season must be eradicated by the time we play our first match," he told WalesOnline.
"We won't get a second chance then. Mistakes will be punished.
"But we've worked hard to achieve Premier League status and we'll do everything possible to stay there.
"That's the first aim and anything above that is a bonus."
Campbell, who scored seven goals in nine starts for the club in the Championship last season, will look to play a part as Cardiff continue their warm-up campaign with a run of tough fixtures against European opposition.
Malky Mackay's men take on Serie A outfit Chievo on Saturday before facing La Liga side Athletic Bilbao a week later.