The club went into administration on Friday, Rooney earlier revealing he only found out about the news whilst watching TV.
Derby now face a 12-point deduction as they've been unable to find a new owner, which could increase to 21 points with a separate investigation into Financial Fair Play breaches.
Yet despite the devastating news, Derby still managed to pull off a win at Pride Park against the Potters.
Rooney was asked by talkSPORT how draining the past 24 hours have been, the Manchester United and England legend said he was more concerned for the club's fans.
"Not [draining] for me," Rooney responded. "For the fans, for the fans who were in the stadium, fans who were at home. It's brought a lot of pride to them fans and they know they can be proud of them players today."
Max Bird scored his first ever goal for the Rams in stunning fashion, before Curtis Davies quickly extended the home side's advantage. Tom Ince pulled a goal back for Stoke in the second half but Derby saw out the win.
Rooney spoke about his pride over the team's performance, but admitted things are only going to get harder.
"We're in for a tough week, I know that," Rooney said. "But to see the players putting that effort in and getting the three points was massive, and I can't stress how proud I am of them players for that performance today.
"I have to keep doing my job, keep preparing the players, getting them ready and again we're going to have some tough moments, I know that, I understand that.
"But I can't ask for anything more than what the players have given me and I think those players will get a lot of credit for the performance and the attitude today and they deserve that."
Rooney moved to Derby as a player in January 2020 after leaving DC United, and retired from the game to become the Rams' full-time manager a year later.
Things haven't gone brilliantly so far, with the side narrowly avoiding relegation from the Championship on the final day of last season.
But Rooney has confirmed he wants to help the club through their current difficulties, and return stronger.
"I'm committed to this football club," Rooney added. "I care about the players, I care about the staff I work with and I'll do everything in my power to help us get through this.
"There will be difficult moments, we know that, but we will come out the other side for the better.
"It might take a bit of time but we will, and I have to just keep preparing the team and getting the players ready to go and try and take points from games."
Rooney was then asked about his management career so far, and if it could have possibly been any harder, to which he managed to crack a joke.
"I'm going on the pro licence course next month so I think I should be getting an honorary one for what I've had to deal with the last 10 months or 11 months," he said.
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