Nuno Espirito Santo's men sealed their title success last weekend thanks to a resounding 4-0 win away at Bolton Wanderers.
Santo's side are 12 points clear of Cardiff with two games remaining, although the Bluebirds do have a game in hand over their rivals.
Wolves are currently on an eight-match unbeaten run and Santo is already planning ahead for next season, while some sections of the media believe they will have enough to avoid the drop.
While Coady is proud to have reached the top flight, he insists the squad just want to enjoy their success for the time being.
He told the club's official website:
It was a really happy day for me, it was such a great feeling. In front of nearly 5,000 Wolves fans as well, it was special for me.
"We’re champions - that’s what we wanted to do, we wanted to win the division and win the trophy and we can’t wait for next Saturday now.
"We’re looking forward to next season - we’re enjoying the moment that we’re in now because it’s no mean feat getting promoted from the Championship with it being such a tough division.
"To do it the way we have, is excellent! I always had belief in this club that it was going to move forward. There’s a great infrastructure in place now from top to bottom
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