The Reds' next match is a trip to Selhurst Park to face Crystal Palace on Monday and given the way Liverpool performed defensively on Sunday, Alisson will be hopeful of keeping another clean sheet.
They saw off Guardiola's men in the Champions League last season, and a title challenge is now on the cards.
Liverpool beat City in three of their four meetings last season, but the key to a title challenge will be a consistency Klopp has so far failed to nail in almost three years in charge.
"We can not be anything other than "the challenger" because we didn't win anything since I don't know when - certainly since I am here".
"He was very unlucky in some seasons with so many injuries, but he continued being a different player", said Pellegrini.
"They will be judged on actually winning a trophy with that team that he's assembled".
Liverpool's next league game sees them take on Crystal Palace on August 20.
The £67m Alisson - briefly, incredibly, the most expensive goalkeeper in the world - is billed as the long-term solution to an enduring Liverpool problem.
And Klopp was delighted with what he saw from the new Liverpool FC signing as he produced an impressive performance against the Hammers. "I play in an attacking position, it's what I get judged on (scoring goals) and that's all". Liverpool, on the other hand, already looks like the finished product.
Two of their potent forward trio picked up where they left off last season, and you're inclined to think they might even be more deadly, given the greater support and solidity behind them.
"We were good friends at Monaco and he was one of the best players there".
'I also didn't think he would have the impact on Liverpool's defence that he's had. They played better than us.
The Estonian was signed for just £4.2 million in 2016, and has one year left on his current contract-though Liverpool have the option to extend this by a further season.
Raheem Sterling and Bernardo Silva scored as City began their title defense with a 2-0 away win that spoiled Unai Emery's debut as Arsenal manager. After that, a clear goal offside decided the game with the third goal.
'He has a lot of help from the players around.
"I think Liverpool played better than us. That's the expectations. Ours is the highest but we know that". But at the moment all three seem locked in an unhappy marriage ahead of a season that Mourinho himself has predicted will be a "difficult" one.