Arsenal looked threatening in the first half, and Martin Ødegaard missed a gilt-edged chance just after half time.
However, Diogo Jota and Roberto Firmino fired Jurgen Klopp’s men to a 2-0 victory to put them one point behind Manchester City in the table.
After the match, Barnes, who won the First Division and FA Cup twice with Liverpool, gatecrashed football reporter Rahman Osman’s post-game video and gave his thoughts.
He told LondonWorld: “First half, Arsenal were the better team.”
But gave a damning verdict on the Gunners’ performance after half time.
Barnes said: “Second half, men against boys.”
The attacking midfielder - who scored a famous goal for the Three Lions against Brazil in the Maracana - also complimented Arsenal’s Thomas Partey.
He added: “I thought Thomas Partey did will in the first half.”
Barnes’ views matched up with LondonWorld’s Rahman Osman who gave his post-match verdict.
He said: “Arsenal started really well, had a really good first half.
“But the second half, Liverpool tweaked a few things and their class told.
“Arsenal are developing and growing and trying to build something, so you can give them that.
“This has been a very good start to year, the first loss since the start of the year, so it’s been a good period for Arsenal.
“Top four is still in their hands, but they’ve got to start beating the big boys.”
Arsenal manager Mikel Arteta said he thought the Gunners have closed the gap on Liverpool “a lot”.
After the game, he commented: “I don’t think the result reflects the performance of the team.
“From box to box I think in many moments we were the better team and did everything we planned.
“I’m pleased how the team has performed, I understand how difficult it is to play against this incredible team and how we have exposed them is not easy at all.
“The way the boys performed showed their courage to play the way we wanted to play, the intensity, they really raised their level.
“But unfortunately games are won in boxes and that was the obvious difference.
“I don’t think there was any other difference in the game apart from that.
“We have closed the gap a lot [on Liverpool] but it wasn’t enough because we opened the door and they went through the door.
“I’m not happy with the goals we conceded.
“When you have the chances against them you have to get something out of it.”
The Gunners will hope to get back to winning ways against Aston Villa on Saturday, and look to solidity their Champions League aspirations.