The Iron overturned a 3-0 half-time deficit and went on to beat their Championship opponents 7-6 in a penalty shoot-out at Pride Park.
Knill, whose team struck twice in injury time to draw level at 5-5 at the end of 90 minutes, said: "I can't think I've ever seen anything like that. That has to be the most remarkable match I have ever seen.
"I can't get my head round it. To be honest, it was a horrible game from start to finish and I already feel as though I've been through half a season's worth of emotion.
"We didn't get a tackle in for 45 minutes but when you are in trouble the only thing to do is go forward and have a go. That's what we did and by the end of normal time I felt we were well on top.
"I was confident about our first five penalty takers but wondered how it would go when we got down to the next lot - the ones who were hiding and didn't want to do it.
"In the event they all looked full of confidence and did the business."
Richard Keogh, Jake Buxton and Theo Robinson gave Derby a seemingly unassailable three-goal lead at the break before Scunthorpe striker Andy Barcham pulled one back seven minutes after the restart.
Buxton headed home his second within a minute to restore the Rams' three-goal cushion, but the Iron hit back through Mike Grella, in the 63rd minute, and Bobby Grant 10 minutes later.
Scunthorpe goalkeeper Sam Slocombe kept out Robinson's 72nd-minute penalty after David Mirfin's foul on Keogh.
Nathan Tyson headed home Derby's fifth goal in the 83rd minute, but Scunthorpe were not finished and grabbed a fourth through substitute Connor Jennings in the fourth minute of injury time and an equaliser two minutes later when Grant slammed home a penalty following Michael Jacobs' foul on Josh Walker.
Derby manager Nigel Clough said: "We haven't even started our league programme yet and we are already feeling rotten.
"This was an absolutely bizarre game. We had enough chances to score 15 goals and that was the main failing as far as I am concerned."