The 35-year old defender, who will retire at the end of the season, could not help his Reds teammates produce a winning result over Everton at Anfield today.
Liverpool were held to a 0-0 draw and although Carragher would have liked more, he had to settle with what he felt was a just result.
"It's a fair result. It wasn't to be and a draw was a fair result,” he told Sky Sports 1.
"There weren't too many chances at either end. It was a tense derby if you like and credit to Everton.
"Coming to Anfield and getting a draw is a good result. I'm slightly disappointed but a fair result in the end I think.
"It was a good day. I've got a few games left with Liverpool. It was a big game derby and I would have liked to have won it but ultimately we didn't lose."