Borussia Dortmund and Feyenoord, who contested the 2002 UEFA Cup final, were dumped out of this season's competition at the second-round stage.
On a bad night for German clubs, Schalke also exited on penalties to end Bundesliga interest in the UEFA Cup, though Bayern Munich could still end up in the competition if they finish third in their Champions League group.
Dortmund, Champions League winners in 1997, were humiliated by French club Sochaux, going down 4-0 for a 6-2 aggregate defeat.
Their cause was not helped when Salvatore Gambino was dismissed after five minutes for hauling down Santos in the area and Pierre-Alain Frau converted the penalty.
Second-half goals from Santos, Wilson Oruma and Jeremy Mathieu completed a miserable night for the Bundesliga club.
Schalke, the 1997 UEFA Cup winners, were protecting a 2-1 lead against Danish side Brondby but fell behind after 15 minutes when Andreas Jakobsson scored from the penalty spot.
Victor Agali equalised after the break but a Mattias Jonson goal in the 70th minute took the game into extra time before a penalty shootout sealed Schalke's fate.
Dutch club Feyenoord, who won the competition in 2002 and 1974, were humbled by Czech outsiders Teplice. Despite gaining a 1-1 away draw, the damage had been done in a 2-0 defeat in Rotterdam two weeks ago.
Liverpool and Newcastle United maintained English interest in the third round after 1-0 home victories over Steaua Bucharest and FC Basel respectively, but Manchester City were knocked out on away goals following a 0-0 draw in Poland against Groclin Grodzisk.
Spanish clubs fared well with Barcelona, Real Mallorca and Villarreal all progressing.
Barcelona's 2-0 home victory over Panionios completed a 5-0 aggregate win, Mallorca advanced despite being held 1-1 by FC Copenhagen, and Villarreal scraped through despite a 1-0 defeat at Torpedo Moscow.
Serie A club Parma bounced back from a weekend defeat by lowly Empoli to thrash Salzburg 5-0 and complete a 9-0 aggregate victory, Benito Carbone scoring twice.
AS Roma were pushed harder, however, needing a late goal from Antonio Cassano to knock out Croatian side Hajduk Split.
Red Star Belgrade, the 1991 European Cup winners, were eliminated by Norwegian champions Rosenborg Trondheim, losing 1-0 in front of a stunned 53,000 crowd.
Russians Spartak Moscow also suffered a shock 3-1 defeat at Dinamo Bucharest, but went through 5-3 on aggregate.
After Turkey's elimination from Euro 2004 qualifying, Gaziantepspor and Genclerbirligi restored pride with impressive away victories.
Gaziantepspor won 3-1 in Lens for a 6-1 aggregate thrashing of the French club, while Genclerbirligi eliminated Sporting Lisbon with a 3-0 victory.
Benfica, however, did keep the Portuguese flag flying with a 2-0 win at Norway's Molde for a 5-1 aggregate success.
