The 35-year-old is set to retire after the Reds' game against QPR at Anfield on Sunday, after making 736 appearances for the club so far.
And while he admits he has been lucky to have had such experiences as a Champions League win in his career, Carragher admits it is disappointing not to have won the title.
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"We weren't good enough, all of us. It's very simple, there's no fancy reason or excuse, other teams in that particular season were better than us.
"A couple of times we went close but it was Manchester United or Arsenal. It's not something I lose sleep over. I've been very lucky to achieve some of the things I have.
"If you look at everyone there's always something someone hasn't done. There's always more to achieve, whatever you've done. I'm pleased with how it's gone.
"If someone had offered me to be here until the end of my career - the trophies, the big games we've played and won, the stadiums I've played in - I'd have bitten their hand off for that."
When asked for his personal highlight, Carragher revealed winning the Champions League is by far and away his best moment in a Liverpool shirt.
He added: "Istanbul, nothing will beat that - the Champions League final. It's difficult to ever top that. We've never won the league, which is a disappointment; if we'd have won that maybe I could compare the two.
"We've won FA Cups, [League] Cups, the Uefa Cup but nothing compared to the Champions League. It's the biggest and best trophy that you can win in club football. It's what we achieved.
"It's a team game; there are different managers and coaches who have helped you along the way, you do your best - I've done alright."