The Bluebirds booked their ticket to the Premier League on Tuesday, with a 0-0 draw at home to Charlton Athletic enough to end their 51-year wait for top-flight football.
There are, however, still three games of the season to come and Malky Mackay's men require another positive result to ensure that they will end the campaign as second tier champions.
Gunnarsson told Sky Sports News HD: "The club deserves to be up there. It's a brilliant club. We can't wait.
"But it's not over and done yet, it's not finished. We have still got three games to go and we want to win the league. We are going to go for it. We aren't going to stop now even though we are up."
Gunnarsson has been a regular throughout Cardiff's promotion push in 2012/13 and admits all of those involved with the Welsh club made the most of a party atmosphere on Tuesday.
He said: "It was brilliant to be a part of it. Just really proud to get there in the end. It's just a great achievement and everyone is really happy about it. I'm lucky to be a part of it.
"It was carnage. The fans enjoyed it and it was good to celebrate with them. It was unbelievable. There are no words to describe it."