The 25-year-old signed for Liverpool from RB Leipzig for £60m in 2023 and was the stand-out performer for the Reds last season, scoring 13 goals and providing 12 assists.
"There's always more to come. I'm never happy," said Szoboszlai. "I want to set the example. I want to be an example also for everyone, as much as I can.
"When I signed, I said I want to win everything. That didn't change for a little moment either. It stayed the same.
"I want to win everything that is possible in this country, also let's say the Champions League. I'm ready to go for it."
The Hungary international, who had two years left on his previous deal, has ended speculation surrounding his future after months of negotiations between his camp and Liverpool sporting director Richard Hughes.
Talks accelerated in recent weeks and a deal was agreed and signed this week. The new deal will see him commit his future to Liverpool to 2031, with both club and player believing that Szoboszlai's best years are still ahead of him.
In February, Mohamed Salah, who left Liverpool at the end of the season, described Szoboszlai as "one of the best players in the world".
With Andy Robertson leaving Anfield this summer, Liverpool need to appoint a new vice-captain and, now his future is resolved, Szoboszlai will be a strong contender to take up that role. He captains his national side.
Szoboszlai returned to Merseyside on Tuesday for pre-season training and will be part of Liverpool's touring party when they travel to the United States for their pre-season tour next week.
For all the talk about new signings - of which Liverpool will certainly make more this transfer window - Szoboszlai's new contract will be one of the most important deals in Andoni Iraola's first summer at Anfield.
Szoboszlai is a brilliant footballer and Liverpool see him as a future leader. Securing his services with his best years ahead of him is a much better look for the club after the way they lost Trent Alexander-Arnold and Ibrahima Konate to Real Madrid.
With the dressing room losing the likes of Salah, Robertson and Konate this summer - and Alisson and Virgil van Dijk's contracts expiring in 12 months, Szoboszlai's long-term commitment is a massive boost for the club and underlines their commitment to retaining their best players.
Liverpool had a forgettable 2025-26 campaign, but the Hungarian was named as their player of the season after a stellar individual campaign.
At various times, his leadership qualities were praised by then head coach Arne Slot too.
Asked if Szoboszlai has the attributes to be a future leader, Slot said: "Yes, but he is still young.
"There is still a step to make in terms of leadership, being vocal and a voice in the dressing room if I compare him to Virgil."
Go back to 2023 when Szoboszlai signed for Liverpool under Jurgen Klopp. Klopp's verdict then was that "this is a signing for our present and also for our future".
Szoboszlai will now be at Anfield for the foreseeable future.