Not so fast, Liverpool: as these teams proved, you don't have to be down in the dumps even after the worst of first legs...
5. Inter vs Bayern Munich, 2010/11 (0-1, 3-2)
As if beating Bayern in the previous May's final wasn’t enough, Inter became only the second side in the Champions League era to overturn a first-leg home defeat.
Mario Gomez had netted an injury-time winner at San Siro three weeks previously, but despite another from the German and a Thomas Muller chip before half-time in the second leg, Samuel Eto’o, Wesley Sneijder and Goran Pandev strikes saw the Italians through on away goals.
Awaiting them in the quarter-finals was a 7-3 aggregate humping from Schalke, who finished 35 points behind champions Borussia Dortmund in that season's Bundesliga.
4. Bayer Uerdingen vs Dynamo Dresen, 1985/86 (0-2, 7-3)
In this West vs East Germany Cup Winners' Cup quarter-final showdown, the pressure was on Dresden after the Stasi insisted they got to the semi-finals. After a 2-0 home win, progress was a formality when Dynamo led 5-1 on aggregate at half-time, in part thanks to Ralf Minge’s first-minute goal (stop sniggering at the back there).
But Uerdingen then scored an implausible six goals in 30 minutes to progress, much to the Stasi's anger. Dresden striker Frank Lippman fled to GDR and never returned; coach Klaus Sammer was fired for bringing shame on the nation. Uerdingen were beaten in the semis by Atletico Madrid.
3. Monaco vs Real Madrid, 2003/04 (2-4, 3-1)
When Madrid loaned Fernando Morientes to Monaco, they felt it would give the forward the exposure necessary to land a big-money move the following summer. Little did they know that it would be their own man who would dump them out of the Champions League.
After netting a crucial away goal in a 4-2 Bernabeu defeat, the striker powered a header past Iker Casillas in the second. With Ludovic Giuly goals sandwiching the Spaniard’s strike, Monaco progressed on away goals.
2. Deportivo vs Milan, 2003/04 (1-4, 4-0)
“For the first and only time in my life, I wondered if my opponents were on something.” So said Andrea Pirlo after his Milan side were bundled out of the Champions League.
After winning 4-1 at San Siro, Milan collapsed in Galicia, with Walter Pandiani, Juan Carlos Valeron, Albert Luque and Fran netting to send Deportivo through. Coach Javier Irureta fulfilled his pre-match promise to make the 35-mile pilgrimage to the catholic shrine in Santiago de Compostela if his team overturned the deficit, though he did so on foot, rather than his original pledge to do it on his knees. Lightweight.
1. PSG vs Barcelona, 2016/17 (4-0, 1-6)
It was over. Barcelona were gone. Dead. Buried. Paris Saint-Germain, in their fifth season of trying, would be claiming a giant scalp in their quest to progress beyond the quarter-finals – but in the end they didn't even get that far.
They really couldn't have asked for much more in a first-leg trouncing of the Catalans; two goals in each half, and denying an away goal in reply. So how on earth, then, did they manage to balls it up from there? No side in the history of the competition had overturned a four-goal deficit, but that's just what Barça managed in a madcap second leg that defied belief.
For a while it followed script: Luis Suarez got an early goal, then Layvin Kurzawa put through his own net before half-time. Lionel Messi plundered a penalty five minutes after the interval. Three-nil, 40 minutes remaining and PSG were on the ropes – this really could be done the easy way.
But then disaster: the reeling Frenchmen grabbed an away goal through Edinson Cavani, and Barça's dreams appeared dashed. They would now have to score three times in the last 27 minutes of normal time to go through, 25 of which they spent not scoring any goals. But no matter: in the 88th minute, Neymar converted a peach of a free-kick; in the 91st, he coolly slotted home Barça's second penalty of the night. Then, ridiculously, in the 95th minute, the brilliant Brazilian chipped one over PSG's backline for Sergi Roberto to score past Kevin Trapp. Bonkers.