Having secured the League Cup in February, the Merseyside outfit will do battle with Chelsea on Saturday in the FA Cup final at Wembley.
And Gerrard expresed his belief that lifting trophies is just as important as maintaining a healthy position in the league.
"It is a successful season. This club is all about winning big trophies and the FA Cup certainly comes under that," he told reporters.
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"We will assess the season after the weekend. If we can look back and say we have won two cups we will be happy.
"But of course we still have to address the problem of our league position.
"Some of the biggest experiences myself and Jamie have had over the years have been winning cups. They are nights when you are successful you look back on with fond memories.
"The FA Cup is special altogether but we got a taste of success winning the [League] Cup and that will help some of the younger players in the squad and everyone really because winning breeds confidence."
Carragher also hailed the importance of cup competitions, claiming that his winners medals are what he will look back on when his career ends and not league positions.
"We had gone five or six years before this season without a trophy and in that time we have had some great nights - European Champions League nights - but at the end of your career you want trophies to look back on as well," the veteran defender opined.
"We have one this season and if we get two, having been in three competitions, that will be a great season."
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The Bootle-born centre-back also said that, despite being delighted by League Cup success, he would view an FA Cup victory as a greater achievement.
He added: "Playing for Liverpool in a cup final is special but we realise playing in an FA Cup final is a bigger stage than the [League] Cup final.
"It is fantastic for the club, supporters, manager and players. It is something to look forward to."