The England legend, 36, left his role with the Rams on Friday following 19-months in charge.
The Manchester United icon was hailed for his leadership in such difficult times last season, which saw Derby suffer a 21-point deduction for entering administration and breaching EFL accounting rules.
However, former Crystal Palace owner and talkSPORT host Jordan believes Rooney should have stayed put following the Rams' relegation to League One as he may find it tough to get another role at a higher level.
"He will have learned a lot from this," Jordan said on talkSPORT.
"Someone asked me earlier on if that means he's a shoo-in for a Premier League job. They've bumped their head.
"He's nowhere near that. I'd be surprised if Wayne got another Championship job any time soon.
"I think he's a bloody fool. You've got a club that's dropped into League One with 28,000 fans that are going to be galvanised up the ying-yang.
"You've got an owner that's coming in there - he's bought the stadium too, so he's not mucking about - I think he [Rooney] is a fool.
"If he thinks his currency's going to get better somewhere else, because it's a bit more difficult in League One and it might need a bit more manoeuvring and manipulating.
"League One is not a division full of quality. If Derby can get some players, in the short-term, into the building and build upon it with 28,000 fans and the momentum behind that, you've got to be out of your mind [to leave]. That's the place to stay."
Rooney, who is now having his first full summer break in 20 years, previously claimed Derby needed 'fresh energy' amid their ongoing financial issues.
"Over the course of the Summer I have been closely following developments regarding the ownership of Derby County," he told the club's official website.
"Today I met with the administrators to inform them of my decision that it was time for me to leave the club. In fairness to them, they tried tremendously hard to change my decision but my mind was made up.
"My time at the club has been a rollercoaster of emotions, both highs and lows, but I have to say that I have enjoyed the challenge.
"Personally, I feel the club now needs to be led by someone with fresh energy and not affected by the events that have happened over the last eighteen months.
"I will remember my time at Derby with great pride and affection and would like to thank all my staff, players and of course the fans for their incredible support. I will never forget you and hope to see you all again in the near future and in happier times.
"Finally, I am aware that the club still have interested parties who wish to take over the running of the club. To them I say this, Derby County is a great club with a great history and great fans. I wish you all the best and much success for the future."