The result was the first time in the club's history that it equaled the previous record set by rivals Manchester United.
According to Carragher and Neville, it is still difficult to overtake Manchester City this season, but there are exceptions.
“No, I don't think so,” Carragher said, according to FourFourTwo.
“Sitting here today, it's hard to tell,” said Neville.
The above two clubs underwent different seasons. Last season, Manchester United managed to finish fourth in the Champions League.
Manchester United also reached the domestic cup final before in Erik ten Hag's first season.
Meanwhile, Liverpool were flopped in the league until they ended up in fifth place.
According to Neville and Carragher, Manchester United and Liverpool could do better in the 2023/2024 season depending on how much budget they spend in the transfer market this summer.
“It all depends on the budget,” Neville said.
“Under the (current) ownership of the club, I think they will probably continue to finish in the top four, but I don't think they will improve,” Neville continued, speaking to Andre Onana.
“If they get a new owner and they have £250 or £300m to spend, they have a chance of moving to number two.”
“I think they have a chance to take this place from Arsenal, but the circumstances have to be used well,” Neville explained.
Even with Carragher, he does not deny that it is difficult for Liverpool to compensate for the mistakes of last season with one summer transfer window.
“Whether they can get back to the level they were before, it's very difficult to face the season they just had,” Carragher said.
“I don't think they can make that jump.”
“But I'm sure Jurgen Klopp will be very energized and determined to put things right after a bad season last.”