The Coca-Cola Championship strugglers stunned the home support as they effectively wrapped up a place in the fifth round by half-time, racing into a 3-0 lead courtesy of a Simon Whaley strike either side of goals from the impressive Karl Hawley.
Rams substitute Rob Earnshaw pulled one back early in the second half but it was scant consolation, who will hope their takeover by American investors can improve the club's fortunes.
A miserable day for Paul Jewell's side, who have not celebrated a home victory since September 17, was completed in injury-time when Lewin Nyatanga was sent off for a professional foul on Neil Mellor, who then converted the resulting penalty.
"We felt as if we had a chance," Preston boss Irvine said. "There's no way we felt that we were favourites coming into the game.
"We knew that if we could keep a solid shape and that if we could be clinical when we got chances then we would have a chance of winning the game.
"But there's no way I thought beforehand that I would be sitting here talking about a 4-1 win.
"I felt right from the beginning of the game we controlled the possession. We passed the ball well.
"We started the game very much in Derby's half and it took quite a while before they caused us any problems at the back, so really right from the start I felt we set off very well.
"We kept possession well and we had a threat about us."
The home side's performance was one even the Rams' most loyal supporters will find difficult to stomach, with the ever-increasing prospect of a return to the Coca-Cola Championship all that remains for them to contemplate.
"I'm at a loss to explain it," said Jewell. "I see them Monday to Friday in training and they're totally different people.
"They come out on a Saturday on match day and they fall apart at the first sign of adversity."
There is at least hope on the horizon for the Rams after a takeover of the club was successfully negotiated with American investors which should provide Jewell with much-needed extra funds to rebuild his squad.
"One of the reasons I came here was that hopefully there was going to be some American investment coming in," he added. "I have spoken to the investors on a couple of occasions and met them in Manchester so they know it's a tough job. They know what a state the team is in at the moment.
"They, like me, see the bigger picture and the bigger picture here is if we get it right it will take off.
"We had a great season last year. It hasn't happened this season but I'm hoping I'll be sat here in a year telling you about the tough times last year that hopefully made not just me stronger, but the club stronger."