Dudek saved two penalties in the shoot-out to help the Reds win their fifth European crown after they had battled back from 3-0 down at half-time to force extra-time and spot-kicks.
And the Pole says Carragher jumped on his back in the build-up to the penalties and urged him to immitate the "jelly-leg" tactics of legendary Anfield shot stopper Grobbelaar.
"I did a little bit of Bruce Grobbelaar," he told us in the sixth episode of MasterCard's Priceless Moments video series. "If you watch the games, [Bruce] was out of power then immediately he went to save the penalty and I had that in my mind.
"But Carragher came to me just before the penalties and he jumped on my back, he was pushing me like 'Do something, put them under pressure, please put them under more pressure, I don’t know... like Grobbelaar did, you remember'. I said, 'Okay but give me a few seconds because I got the book, and I need to study my penalties.'"
Serginho fired Milan's first penalty over the crossbar, and while Jon Dahl Tomasson and Kaka both converted, Dudek saved from Andrea Pirlo and, to win the cup, Andriy Shevchenko.
"When I do the hands I want to see the player see me doing this," Dudek added. "And [Serginho] shot over the bar and I thought 'it's working, you made him scared, carry on! Carry on, carry on and do something more', and I had the fortune to save some."
There may never have been a shoot-out had it not been for Dudek's miraculous double save at the death, when he first kept out Shevchenko's header and then, somehow, the Ukrainian's follow-up from just yards out.
That moment was voted the best in Uefa Champions League history by Uefa readers, and Dudek says it was a big moment in his career.
"It was a crucial moment, he added. "It was the last minute of extra-time. I thought there were two different players shooting at me, it was incredible.
"Straight after that I was thinking to myself, 'this is the moment you were waiting the whole of your career for, the whole of your football life'. But there was penalties."
Dudek went on to become the hero of the hour, but although he remembers exactly what happened next, he admits he had no idea that Shevchenko's penalty was so decisive.
"I didn’t even know it was the last penalty, you know. I was taking it penalty by penalty. I didn’t know how Shevchenko was taking the penalty because he scored twice here, twice there, one there and I said, 'Okay I have to wait to the last second'.
"And I went to my right side and he stopped. But he couldn’t stop as long, and he shot. He wanted to change because I was on [the right] side, he wanted to change. He couldn’t do anything more. He just wanted to put inside, like straight in the middle of the goal.
"But I saved it like someone had stopped me from falling down. I was in the air for a split second, waiting for this ball and I caught it in my hand, I flipped over and I saw the people running at me, and I thought 'okay it must be finished!' It was the most beautiful moment."Check out the video above for the full interview with the former Liverpool and Poland goalkeeper.