The old European Cup (which hasn't existed for well over 30 years) allowed for some laughably easy runs. Nothing like the prestige now of winning the Champions League where it is basically impossible to fluke your way through to the semi or even the final with soft draws.
Just to pick five examples:
Liverpool in 76/77: Crusaders, Trabzonspor, Saint-Etienne, FC Zürich, Borussia Mönchengladbach
Forest in 78/79: Liverpool (fair enough), AEK Athens, Grasshoppers, Köln, Malmö
Villa in 81/82: Valur, Dynamo Berlin, Dynamo Kyiv, Anderlecht, Bayern München
Liverpool in 83/84: Odense, Athletic Bilbao, Benfica, Dinamo Bucharest, Roma
Liverpool in 84/85: Lech Poznan, Benfica, Austria Wien, Panathinaikos, Juventus
It was simply nowhere near the quality of what's on offer now, especially as many countries that now have decent domestic leagues were massively weak at the time (Turkey and Portugal in particular, and with the Soviet league being what it was, loads of good teams from there missed out because of there only being one spot available).
Not to say that the CL format that existed before this season or the current one are perfect, but the challenge isn't even close to comparable. And seeing Man City play Larne or TNS over two legs wouldn't be very good to watch.