Campbell spoke at a news conference Friday, one day after negotiations were completed on a five-year contract extension reportedly worth $55 million with $31 million guaranteed.
The 6-foot-8, 300-pound defensive lineman led the Cardinals in sacks with eight last season. He had 72 tackles and blocked three field goals. Campbell forced two fumbles, recovered one and intercepted a pass.
Campbell was drafted by the Cardinals in the second round out of Miami in 2008, the 50th player chosen overall.
"I still have a long way to go," he said. "I'm 25, still a young guy, taking it one day at a time."
He said that while there was uncertainty about a long-term contract, he trusted the advice of his agent Ben Dogra.
"He reassured me that it was a long process, but it would get done and I'm really proud of the outcome," Campbell said. "I tried to do my best taking my mind off of it and let it play out the way it was supposed to."
Campbell is considered an integral part of a defense that emerged as the team's strength as Arizona went 7-2 after stumbling to a 1-6 start last season. After what was easily his best NFL season, Campbell said he has plenty of room for improvement.
"I made a lot of mistakes last year, too," he said. "Watching the film, breaking it down, I definitely could be a lot better."
Campbell said he doesn't mind the pressure of living up to his new contract.
"I like having pressure on me," he said. "It makes me work even harder."