Nuno Espirito Santo's side secured promotion with four games to spare at the weekend, and are now looking to wrap up the Championship title before looking forward to Premier League football at Molineux next season.
Coady, now coming to the end of his third season at Wolves, believes that the team's achievements stem from the 'brilliant' way in which the clubs operates.
"It's a brilliant club to play for," Coady said. "This promotion is a culmination of a lot of things - it's a fantastic club coming together. This is how a club should be run. I've been here for a few years now and I've played for other clubs in the past, and this club is now properly - everything is there for us, absolutely everything.
"A lot of people have had a lot of things to say about us this season but the boys have played with smiles on their faces and they've not said a word about anything. We know that the club is run brilliantly and now we can hopefully go on to bigger and better things."
Coady explained that Wolves' approach of leaving no stone unturned even extended to the moments after promotion was sealed via Brentford's late equaliser against Fulham on Saturday evening - a game which the players watched together as they prepared for Sunday's clash with Birmingham.
"We had a little bit of a celebration on Saturday and that was fantastic, but straight away the manager held a meeting to reinforce that we had a big game the next day, and as a derby, it was vital for our supporters," Coady said.
"With the manager we've got, it wasn't difficult to stay focused - he focuses you every single minute of every day, and that's what he's been like all season. We wanted to win against Birmingham so we prepared right for it - we prepared like we had done for every single other game."
The preparation paid off, as Wolves ran out 2-0 winners before celebrating with the home fans at Molineux. Coady believes that, while a determination remains to accumulate as many points as possible in the three games that remain, the final weeks of the season should be enjoyed by everyone connected with the club.
"Promotion is a massive thing for this football club," he continued. "As a club, we've been out of the top division for too long, and it's not been good enough. We can forget about that now though - we've had a hell of a season and we're going to enjoy the last three games.
"We want to do well in them, but we also want to play with smiles on our faces like we have done all season.
"You dream of this at the start of the season, so now is a time to get excited. We're not looking too far ahead but we know we've done fantastic things this season and that it's huge for the club to be back in the Premier League. I'm sure everyone, especially the supporters, is excited about what next season will bring."