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This was a tough night in all respects for Liverpool, who will certainly question the luck of the Champions League draw after topping the new format's table with ease only to draw a PSG side who can now be considered potential winners, such is their quality.
If Liverpool rode their luck to somehow escape with a 1-0 win in the first leg in Paris, they did not enjoy the best of fortune here as both Alexander-Arnold, injured and now a doubt to face Newcastle United at Wembley, and Jarrel Quansah hit the woodwork.
Donnarumma also saved well from Ibrahima Konate and Luis Diaz, while Mohamed Salah had a rare night when the final flourish eluded him.
Liverpool's luck did not even hold for the toss for penalties, the kicks being taken in front of PSG's fans at the Anfield Road end rather than in front of the Kop, who were forced to try and inspire from afar.
This was the first time Liverpool had gone out at Anfield after winning the first leg of a European tie, while it was also the first time they had lost a penalty shootout in this competition after winning the European Cup against Roma in Rome in 1984, the Champions League against AC Milan in 2005 then beating Chelsea in the semi-final in 2007.
PSG will say, with some justification, they deserved their win over two legs and coach Luis Enrique, a Champions League winner with Barcelona, is presiding over a superb revamp of a team that looks more cohesive and energetic than the one that failed so often in the Champions League.
The "Bling Bling" era of Lionel Messi, Kylian Mbappe and Neymar has gone, to be replaced by Ousmane Dembele finally fulfilling his potential and recent signing Khvicha Kvaratskhelia adding a new dimension.
This is a team that will threaten every opponent.
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