The Sky Sports pundit also claims the German “lost” the argument due to a lack of evidence, with the Reds playing a game every 5.4 days this season - compared to 4.5 days last season.
James Milner’s injury is the latest in a lengthy list of absentees for the Premier League champions, which has included the season-ending injury to Virgil van Dijk.
And Neville believes Klopp is aware that the biggest risk to Liverpool not defending their title is to lose another key player to injury, pushing him to raise the issue of fixtures publicly, with his side currently joint-top with Tottenham.
“The biggest risk to Klopp winning the league again this season is another big injury or two,” Neville told Monday Night Football on Sky Sports. “So, he wants to try and gain that advantage to put some psychological thing into people's minds. Sir Alex Ferguson did it for 15 or 16 years.
“Klopp has been the best manager in interviews for the last few years, he's been the best manager on the pitch, he's connected with the fans better than anybody else, his style of football is fantastic, but on Saturday he got done in an interview, and that's very rare.
“He didn't get his story right, he hasn't got his evidence to back him up either in games played or in the Saturday kick-off slots. He just lost this particular one having been brilliant in all his other interviews that he's done.”