Kenny Dalglish's side ended their six-year trophy drought following their win over Cardiff City on Sunday as they edged victory through a penalty shootout after the Championship side were able to hold their Premier League opponents to a 2-2 at the end of extra time.
Despite Liverpool enjoying the majority of chances, Kuyt praised Cardiff for their performance in the final and hopes his side can now go on to lift more silverware as they still remain in the FA Cup.
“They [Cardiff] were very impressive. I've got lots of respect for the manager, the team and the supporters," Kuyt told Sky Sports.
"All I can say is, they [Cardiff's fans] deserve more, but we wanted this trophy so desperately and hopefully many to follow for the club now.
“It's unbelievable, this is why I came to Anfield. To get my first medal at Wembley is great and hopefully we can get one more later on in the season.”
Kuyt admitted he was unhappy at being benched for the final at Wembley but insists Liverpool's performance was worthy of claiming the League Cup crown.
“It was an incredible day.” Kuyt said. “I'm very disappointed not to play longer than 50 minutes, but you have to put it aside.
"I was so happy to score the goal, and then, I think it was 30 seconds before the end of the game, I cleared the ball off the line and thought 'this is it'. Then the other corner went in, and it ended up with penalties.
"The team worked really hard but the most important thing was that we kept believing and I think at the end of the day we deserved this trophy.
“We kept believing. I walked to Stevie and said 'listen, there's a few more to take and we can get back in the game' and we did. Like I said, belief is the most important thing in football and that's what we had.
“I knew I had to score my penalty or else it was over, but it's always the case – you just need to do one thing, and that's shoot the ball in the net, and that's what I did.”
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