Jurgen Klopp is dreaming of a Europa League final meeting with former club Borussia Dortmund after denying Manchester United a place in the last eight.
Louis van Gaal's hosts turned in a marked improvement on their showing in last week's first-leg defeat at Anfield and deservedly led through Anthony Martial's penalty after 32 minutes.
But a dazzling solo effort from Philippe Coutinho gave Liverpool a crucial away goal and there was no way back for United as their challenge faded.
Dortmund breezed to a 2-1 victory at Tottenham for a 5-1 aggregate triumph and Klopp revealed his former colleagues are keen to wait for a Liverpool meeting until the final in Basel ahead of Friday's quarter-final draw
"All my friends in Dortmund want to play us - but only in Basel," he told BT Sport. "They won at Tottenham, not too bad.
"When you saw all the results there are only good teams in the race. It's cool, last eight - perfect."
Klopp marvelled at the intensity of the match and atmosphere in the first leg and the one-time proponent of "heavy metal football" was satisfied by the spectacle once more, reserving special praise for Coutinho and his centre-back pairing of Mamadou Sakho and Dejan Lovren.
"It was nice and intense. You could see, you could feel the atmosphere again," he said.
"It was an intensive game. They tried to play really offensive, but we had our chances. It was Liverpool against David de Gea. It was unbelievable what he did again.
"We scored an unbelievable situation from Philippe Coutinho. Fantastic. The game changed.
"He had another situation where we had a brilliant offensive situation. He is a young lad still but he thinks about [the game], you can see in his face.
"Sakho and Lovren were not too bad to be honest. They had to find legal solutions which is sometimes not so easy."
Klopp was forced to take his captain Jordan Henderson off during the second half and offered a graphic explanation.
"Jordan Henderson was ill," he added. "Can I use the word 'vomiting'?"