Dominance was there of course, but I think Sloth will not be satisfied with how Liverpool allowed Bournemouth to come back into the game in their home stadium. They became slightly sloppy after their 2-0 because normally they could lead by 4 goals instead of 2 if they had taken their chances seriously. For a few minutes during the game after that dominant start, I had the impression that some of the Liverpool players were celebrating the win already. That is not how a coach wants his team to go about comfortable leads.
Yes, I agree with you, that in this match, Liverpool's players were too complacent because they felt they were ahead. But in the end, all of that nearly resulted in a draw for Liverpool. Fortunately, Liverpool's players quickly recovered and regained the lead through goals from Chiesa and Mohamed Salah. Although Liverpool ultimately won this match, things like this shouldn't be allowed to continue. It would be very dangerous if Liverpool displayed this kind of performance against strong teams like Arsenal or Chelsea. When great teams are given the freedom Liverpool gave Bournemouth, it becomes a very serious threat. 
Therefore, Arne must immediately correct this and prevent a repeat in future matches. Especially in the upcoming match, Liverpool will play Newcastle, which will certainly be more difficult than Bournemouth.
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Right and while I still think the most important first step is to get the three points and have a calm beginning of the season, a team like Liverpool could still send a message with that first game. Showing others that they are vulnerable like that and a team like Bournemouth can turn that game into their favour within minutes at Anfield Road is not what they should aim for. Some will say a win is a win, but kicking off a season with a bang can have an effect. If they win this game like 4-0 or 5-0, you instantly know that the next team that has to play them at Anfield Road knows that the g ame won't be funny for them and they won't have many chances.
Manchester City had a different challenge to tackle. It was about not losing any points and the clean sheet is what they needed while Haaland scored two goals and begins the season with good feelings. It is good to see Manchester City was playing decently.