Jürgen Klopp's men claimed the prize after lifting the Premier League title in July to end the Reds' three-decade wait for the top-flight crown.
Following up their Champions League triumph in June 2019, the team clinched the league in 2019-20 with a record-breaking seven games to spare before then amassing a club-record points total of 99.
Also in the same campaign, Liverpool lifted the FIFA Club World Cup for the very first time, as well as winning the UEFA Super Cup.
In 2020-21, Klopp's side currently sit top of the Premier League and have extended their unbeaten run at Anfield in the league to 66 games.
Accepting the award on Sunday night, Klopp commented: "I think my team deserves it honestly because they did an incredible job.
"It's a mix of talent, character, desire and plus the power of the club, which is really a big one. That all comes together so we could become champion and it was a great moment, to be honest."
Captain Jordan Henderson added: "It means a lot to the team. Looking from the inside, the lads deserve it because of how hard they work every single day, wanting to improve, push each other to succeed.
"But I'd also like to mention the team that you won't see on the pitch, which I think needs a special mention because they do everything behind the scenes for us to go and perform. The likes of the medical team, fitness team, grounds staff, kitchen staff, security.
"Everybody at the training ground do everything every single day for us to go and play football to the best of our ability on the pitch. Without them, we wouldn't have been successful in the last few years."