Carragher's error allowed Everton to open the scoring in the first-half.
"This was the biggest derby I've played in so I'm delighted the lads have helped me out," said Carragher, who was so wound up about the game that he struggled to sleep for three days.
"It's one of the biggest games I've played in, right up there with the Champions League final. I was close to tears, to be honest. The thought of the stick we would have got on the streets of Liverpool if we'd lost that game... I'm not sure we would have ever recovered."