Liverpool scored in the Emirates a 1-1 draw. Alexandre Lacazette equalized for Arsenal in the last ten minutes.
The result means that the Reds are tied to second-placed Chelsea in the Premier League table and two points behind leaders Manchester City.
Despite their unbeaten start Burley does not think that Liverpool is at the same level as Jürgen Klopp last season.
He claims that they had caused Arsenal more problems when they were the best.
"They seem at least a bit run down in intensity," said former Chelsea midfielder Burley.
"I know that Arsenal went well and Unai Emery is doing some good things right now.
"But they stifled this arsenal team, the mistakes stifled them.
"They did not do that."
Four days after the draw in the Emirates, Liverpool suffered a surprise 2-0 defeat at Red Star Belgrade in the Champions League.
Klopp's side now face a difficult task to qualify from Group C. The games against Paris Saint-Germain (away) and Napoli (home) are imminent.
But Burley is helping Liverpool to get along with PSG.
"If I were PSG, I think I'm relatively confident," he continued.
"If I have Liverpool at home who do not play as well as they did last year, they're in second place in the Premier League, they are two points behind, they are the head of the group, I understand that.
"But they cooked too little, which they were.
"They played PSG (Liverpool) at home and PSG have the worst team in the segment (Red Star), but they are not at home.
"I think if I were her, I would say, listen, here are six points."
"I'll say the PSG got through because they beat Liverpool in Paris and I think they'll do enough in Belgrade.
"With Liverpool at home, I'll say there's Liverpool, too."