Kuyt was glad to beat the Bitters at their own pit on Sunday and now hopes that result will be the springboard to some improved performances from the Reds.
"We're really happy with the result," said the forward.
"It's one of the most important games of our season and to beat Everton always gives you a special feeling. I'm really happy for the team and the supporters.
"A derby is more important than almost every other game, and to win this means a lot for us.
"The result is more important than the performance in a derby. You know it's going to be hard to play football and you need to show character. We beat Debrecen with a clean sheet and we did the same here, so hopefully we bring some of our confidence back.
"It's a good result and hopefully we can take the confidence from this into our next couple of games. It's been a while since I scored, but for me that's not the most important thing.
"When things don't go your way it's disappointing. It has been a very hard period for us but, like the manager says, we have to move on now and look forward. This was a good win, especially as it gets us back in the top five.
"Liverpool have had a great history in the Champions League, including the three years I have been here. We have had some special nights and we want them again.
"We needed to win, and that's what matters most. This win has come at the right moment for us. Everybody knows that we have struggled in the Premier League this season and haven't done well in the Champions League. But we have to move on."