The Brazil international and his Paris Saint-Germain team-mates made the trip to Anfield for their Champions League group-stage opener on Tuesday night.
The PSG record signing scored four goals in four games in Ligue 1 to help the Parisian club secure top spot in Ligue 1 in the early weeks of the new season.
Neymar, though, struggled to have an impact on the European clash on the Brazilian’s first visit to Liverpool FC’s famous Anfield stadium.
Goals from Daniel Sturridge and James Milner handed Liverpool FC a commanding lead before PSG halved the deficit ahead of half-time.
Neymar’s strike partner Kylian Mbappe appeared to have rescued a point for the visitors with six minutes to go before Roberto Firmino’s winner in added time.
The former FC Barcelona star had 64 touches of the ball but Neymar was muted coming in from the left-hand side.
Ex-Liverpool FC captain Barnes believes Neymar wouldn’t command a place in Jurgen Klopp’s team.
Barnes told talkSPORT: “It depends who the manager is – not with Jurgen Klopp.
“I saw the interview Klopp gave last night, he spoke about the defensive work of the whole team, meaning the front three as well.
“A lot of people say Neymar is the best in the world, which may suit PSG or Man City or Barcelona.
“But regardless of how good he is, there is no way he would suit Liverpool under Jurgen Klopp.”
Liverpool FC lost 3-1 to Real Madrid in the Champions League final in Kiev back in May.
The Reds finished in second place in the Premier League table last term.
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