Kelly challenged Klopp in response as the pair went toe to toe in a fascinating interview live on television, and Neville says the Liverpool coach "lost" the argument.
Neville believes Klopp is looking to gain an advantage with mind games as his squad continues to be depleted through injury, but failed.
"The biggest risk to Klopp winning the league again this season is another big injury or two," Neville said on Sky Sports' 'Monday Night Football'.
"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.
— Football on BT Sport (@btsportfootball) November 28, 2020
"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."