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
Real Madrid v Liverpool: A goal to be scored (90 mins) - 40/1 with Ladbrokes. 18+. UK+IRE New Customers Only. Available for a limited time. Min deposit £5. Certain payment methods and cashout excluded. Winning bets paid in cash based on the normal price on our website. Enhanced odds paid in £5 free bets. Free bets valid for 4 days. Free bet stake not returned. T&Cs Apply.
40/1 Real Madrid v 60/1 Liverpool with Betfair. New Customers can get Real at an enhanced 40/1 to win 90 mins or Liverpool at 60/1. Max Stake £1. Winnings paid in free bets, valid for 7 days, only deposits with cards/Paypal count. Exchange and multiple bets excluded. T&C’s Apply. 18+|Gamble Aware.
Bore Draw Offer - get a refund on selected pre-match markets if any game finishes 0-0 with bet365.