Milan, who were defending champions at the time and had not conceded an away goal in the competition up to that point, led 4-1 after the first leg before going down 4-0 away in Spain.
City were however, unable to complete the much anticipated comeback as Liverpool hit back in the second half with goals from Mohammed Salah in the 56th minute, and Roberto Firmino putting the nail on the coffin in the 77th minute.
Messi and fellow Barcelona forward Luis Suarez hardly threatened as Roma dominated possession for long stretches and stifled the Catalan club with high pressure. He patted his chest and was mobbed by his Roma teammates. That is the case if we win or lose.
"We knew it would be hard, but we had that little bit of belief", he said.
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Ruben Neves, who is the favorite for the Player of the Year, scored from a free kick in the 67th minute. For Manchester City , it was a second disastrous loss in four days.
Roma are also through to the Champions League semi finals following a sensational comeback against Barcelona. A solitary goal from the Blaugrana would've required Roma to respond with 4 of their own to take the game to extra time, and 5 to win - something that may have well been next to impossible for the Romans.
Trailing 4-1 after last week's quarterfinal first leg at the Camp Nou, Edin Džeko, Daniele De Rossi, and Kostas Manolas all scored to take them through to the semifinals on away goals against all the odds.
Jurgen Klopp side made it 4-1 on aggregate 10 minutes into the second half with a clean Mohamed Salah strike, before Roberto Firmino scored the victor for the night to end the game 5-1 on aggregate. "In the first leg they denied us two penalties but tonight we showed that Roma can play with and beat anyone". "You analyze things", Valverde said when asked if would take the blame for the loss. The former Manchester City man ran beyond Samuel Umtiti to meet De Rossi's pass and toe an untidy finish past Marc-Andre ter Stegen, generating ample noise and belief in the stands. Dzeko got away from the Peak and forced the Spaniard to break the rules. Pique then grabbed Dzeko's left arm and tugged the striker to the ground. Midfielder De Rossi emphatically planted the penalty past Ter Stegen. "[It's the] first time in history - it means that for the club, for me, for all our great fans and we definitely enjoyed this one, but the semifinal will be even better".