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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."
Aaron Wan-Bissaka was applauded off the pitch by Palace fans after his potentially goal-saving red-card tackle
Palace manager Roy Hodgson was furious with the penalty decision - but accepted Wan-Bissaka's red card.
For the penalty, former Liverpool defender Sakho put his arms on Salah and then twice appeared to attempt to trip the forward, who went down.
"We probably did enough to get a result," Hodgson told BBC Sport. "I don't think it was a penalty. I'm angered that a good result was taken from us."
But BBC Radio 5 live's co-commentator at Selhurst Park, Chris Sutton, felt it was a penalty. "There was enough contact," he said. "I can understand Palace fans are frustrated but it's bad defending."
The Premier League is the only one of Europe's top five leagues not to use video assistant referees this season - but even if a VAR official or referee Michael Oliver had the option of watching it again, it may not have been overturned.
The same was true when Wan-Bissaka clipped Salah before he could reach the penalty area. The Egyptian had possibly lost control before the tackle came, and some fans were not convinced about the decision, but Sutton said the referee had "no choice".
Hodgson agreed. "Wan-Bissaka catches him," he said. "I don't think he tried to pull him down but there was contact and he pulled him down. It was the right decision. He was the last man and did his best to rescue the situation. In another game he might have got a toe on the ball. I don't blame him at all."
Liverpool are being widely tipped to sustain a title challenge this season but they were never likely to follow up their 4-0 opening-day win over West Ham with a similar result at Selhurst Park against a team in good form.
But they dominated, having more possession than the Eagles, who were on the back foot for most of the game.
Salah, who scored 44 goals last season and once on the opening day, did not look at full sharpness - but he was still involved in all of Liverpool's best moments.
The Egyptian was fouled for the penalty and the red card, had a couple of shots blocked and missed with two chips over Hennessey.
And he also set up Mane's late goal after Palace committed players forward for a corner, Salah playing the ball to his Senegalese team-mate, who ran 50 yards before going around the keeper to tap into an empty net.
"In these moments the fuel is really low and maybe the players need a bit of help from an angry manager - 'run or I will kill you' - and they did that with a fantastic counter-attack," said Klopp, asked about his tense demeanour in the final few minutes.
The Eagles, who were unbeaten in seven Premier League games going back to a 2-1 defeat by Liverpool on 31 March, worked hard and had chances but were second best against talented opposition.
Their biggest chance came when Townsend got the ball outside the box and sent a brilliant effort on to the crossbar, with Alisson beaten.
Luka Milivojevic also went close with a free-kick, and Wilfried Zaha, who signed a new five-year deal this week, had a low shot saved in the second half.
Christian Benteke never looked like adding to his two goals in 2018, with one shot from 20 yards flying wildly off towards the corner flag.
Full-back Wan-Bissaka played well and was involved in a good duel with Mane on Palace's left-hand side - and he was applauded off the pitch by home fans after denying Salah a chance to score with his red-card tackle.
Hodgson brought on summer signing Max Meyer for a late debut, but the German was not able to have an impact.
"I thought we pushed them very hard," said Hodgson. "We should have come in at 0-0 at half-time and the second half would have been even tougher. We gave them enough problems and we can consider ourselves unlucky to lose 2-0.
"I'm more interested in the fact we played really well [than talking about the referee]."
Virgil van Dijk was impressive at the back for Liverpool, making a game-high eight clearances and completing 73 of his 79 passes
"I don't know a lot of centre-backs in the world who can deal with Christian Benteke like Van Dijk did," said Klopp after the game.
Liverpool host Brighton on Saturday (17:30 BST), a day before Palace are at Watford (13:30 BST).
