I don't think there is much wrong with Liverpool's current squad, of course the fans are waiting for a new star player to be added to the squad, maybe it could be because it would be an impressive innovation for the championship. But as you said the current squad is good enough to compete with Manchester City and Arsenal.
From last season me to don't see anything wrong with Liverpool squad even next season they can still play well and might still maintain their top three position, and I don't know why their fans are waiting for a new star their will be a lot of consideration before the club will want to take a step of going for a new player. And it's not as if it won't be useful if they don't buy, but since they did. It make any move I think the fans should just accept that and it will be better that for them.
They played a very good game against Manchester United, Liverpool already gave good signals for the new season with a score of 3-0, so in the end the squad is the same and they are good to be honest.
Manchester United played a very good game, because they are the one that did not win and Liverpool won an they are the one that got the credit. And this is what Manchester United wants to start the league. Preseason they are already conceding 3 goals to nil, Liverpool have shown that they are still in position to perform better this season we already know were to place Manchester United.