The Reds beat Cardiff at Wembley to claim their first trophy in six years in February, but fell to an FA Cup final defeat to Chelsea and finished eighth in the Premier League with the club's lowest points total since 1954.
"Of course I am disappointed with results in the league, but I would not have swapped the League Cup win for anything as I know how much it meant to our fans and the club to be back winning trophies," Dalglish said in a statement.
Dalglish insists he is proud of his second spell in charge at Anfield, despite admitting that the club's league position was disappointing.
"It has been an honor and a privilege to have had the chance to come back to Liverpool Football Club as manager," he said.
"I greatly appreciate the work that Steve [Clarke], Kevin [Keen], the players and all of the staff put in during my time and feel proud that we delivered the club's first trophy in six years winning the League Cup and came close to a second trophy in the FA Cup Final."
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