The Dutch forward won the Premier League title for the first time with the Reds last season and explained that the team wants to do even better this season.
Gakpo told Sky Sports: "I think, because for a lot of players it was the first time and it being the biggest league in the world it was very special, and an emotional day for everybody involved.
"I think we were all very proud at the time, still are what we did last season but it also gave us a lot of hunger that we want to do it again and again, and even we felt a little bit of frustration that we were knocked out of the Champions League, because then maybe we had something more special."
Liverpool's summer has been overshadowed by the death of forward Diogo Jota and his brother Andre Silva in a car crash last month but Gakpo says the club will do its best to ensure his legacy lives on.
The Dutch international said: "It's always difficult to speak about it, but the fans showed again how much we all loved him and how big a place he has in everybody's hearts.
"It's still tough for every one of us, and we will try to do our best for his legacy and his family, to support whenever we can.
"The club, the fans and the whole football world showed great tributes and we as a team and as a club will try to make sure he lives forever."
Liverpool thrived in their first season under Arne Slot last term and Gakpo thinks that the coach's "calm" approach is useful.
The star said: "He's just very normal. When we start to train or when we do a meeting, he's very focused on what he wants us to do, and what he wants to teach us. He's very serious, very demanding as well, from the quality, from the intensity, but when the training is over and we do maybe a team activity or something, and he's there, he's very relaxed.
"I think everybody likes him as a person. Obviously, when you win, it makes it a little bit easier. Occasionally, like in the derby against Everton, we saw a little bit of raw emotion from the manager, but I think, overall, he's very calm, and tries to speak with logic a lot of times. He doesn't let the emotion get the better of him."
