Sadio Mane and Roberto Firmino added to Chris Wood’s own goal as the Reds ran out 3-0 winners at Turf Moor on Saturday.
The win meant that Liverpool kept their place at the top of the Premier League with 12 points and remain the only side with a 100 per cent record.
Jurgen Klopp’s side are aiming to win the club’s first English league title for 30 years – something they failed to do last year as they came second to Manchester City by one point.
But Barnes, who is Burnley’s top scorer this season, believes beating Liverpool will take some doing this season.
“You can see their quality all over the park, and they are still growing, aren’t they. They are going to take a lot of stopping,” he said.
“They are a better team than when we played them at the start of their winning run – but so are we, although the scoreline might not show that.”
Barnes then spoke of the ease in which his side let Liverpool tear through them to score three times without response.
“We just gave away goals too easily,” he added.
“Their first goal was a freak, the second came from our mistake, and the third came when we were pressing to try to get something out of the game and lost our shape. It was a tough afternoon for us.
“We had a couple of chances, and you have to take those against the top teams, or they will make you pay for it.”
Barnes also praised the way in which Liverpool played with such poise, noting that they took the chances they had to score and weren’t wasteful.
“But you have to give them credit for how clinical hey were for their second and third goals,” the Englishman said.
“That is what Liverpool can do to you – they punish teams because they are so quick on the counter-attack, and so good when they get a sniff of goal.”