It was the forward's 10th strike for the Reds in total and Kuyt was surprised to learn that it was his first since an important header in a famous 2-1 win at Barcelona back in 2007.
Kuyt told liverpoolfc.tv: "It's good to have him back. Was his last goal for us in the Nou Camp? Really? That was a good goal!
"It's like how it was four years ago. It's like he's never been away. We signed here at the same time and used to live close to each other in the beginning.
"We drove up a couple of times to training. That was good. He's a top professional who wants to win every game and help his teammates.
"He definitely had a big role in the game against Brighton and I think he will have a big future for Liverpool if he keeps playing like this.
"He will be very important for us. Every player in the squad is important. We all need each other.
"Everyone wants to knock on the door and play games regularly. It's good to have competition in the squad. That's what you need if you want to challenge for trophies."