However, Barnes believes incoming boss Arne Slot deserves time and the fans' support.
Barnes told the Daily Star of the team's downturn in recent weeks: "The club have had a blip.
"We expect things to happen for Liverpool because of what Klopp has done in the past. But the future looks very bright for Liverpool.
"If you look at how competitive they are in the league, which is the most important barometer for consistency, with a whole new team and a whole new profile of player and then you look at the age of these players. Over the next few years, if this group stays together, they will only improve."
Barnes added: "I think fatigue could be one of the reasons for the drop-off.
"There's been a number of key absentees throughout the season and some players may have played a little bit more than they would have done.
"You have to remember that this is also a new Liverpool team. When you look at the Liverpool teams during Klopp's tenure, the pressing comes from the midfield.
"When we had players like Jordan Henderson, Fabinho, James Milner that was a midfield that was so used to the way that Klopp wanted to play without the ball.
"The press and the trigger for that press from the front players, there was a perfect understanding between the players. All of a sudden, these guys got a little bit older, and a new profile of player came in, guys like Thiago, Harvey Elliot, Curtis Jones."