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The Reds kicked off their defence of the Premier League title with a dramatic victory during which they surrendered a two-goal lead in the second half.
Antoine Semenyo's brace got Bournemouth back on level terms before super sub Federico Chiesa volleyed home in the 88th minute and restored Liverpool's lead.
Mo Salah finished things off with a sublime solo goal, ensuring that the champions made the perfect start - at least in terms of the result.
Carragher was less than impressed with Liverpool's display, claiming that Arne Slot's side had no control just like in the Community Shield last Sunday.
It's absolutely shocking at this level.
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"For Semenyo to run that far and get his shot away is incredible - but where Konate is going?
I don't like it.
"At no time last week in the Community Shield did I ever feel Liverpool were in control of the game.
You can draw 2-2 with Palace, that can happen.
Will Liverpool retain the Premier League title?
If Liverpool continue like that, I don't think they will win the league."
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