Liverpool manager Jurgen Klopp said he was "not interested in sending a statement" to his side's title rivals after victory over Crystal Palace gave them a second successive Premier League win.
The Reds - who finished 25 points behind champions Manchester City in fourth last season - were worthy winners at Selhurst Park and join five other teams, including City, on six points after two games.
James Milner gave them the lead with a penalty after Mohamed Salah was brought down by Mamadou Sakho in the closing seconds of the first half.
Palace had young defender Aaron Wan-Bissaka sent off with 15 minutes left after he brought down Salah when the Egyptian was through on goal.
And Sadio Mane wrapped up the points in injury time when he ran from his own half before rounding Wayne Hennessey to score.
The Eagles had chances, and Andros Townsend curled an effort on to the bar after a mistake by the otherwise impressive Naby Keita.
"It's very early," said Klopp, when asked whether the result confirmed Liverpool's pre-season status as Manchester City's closest title rivals. "I couldn't care less really. We are not in a race with other Premier League teams each weekend.
"It is too strong to say anything after two match days. You can discuss whatever you want - just do it without us."