Twenty-two years later, Xabi Alonso's Werkself have already gone some way to banishing those ghosts by making Bundesliga history, Saturday's 2-1 win over Augsburg completing their unbeaten title-winning campaign.
This week, they have a chance to make it an unbeaten treble, heading to Dublin for Wednesday's Europa League final before taking on Kaiserslautern in the DFB-Pokal on Saturday.
Looking to deny Bayer one of the greatest achievements in recent memory are Atalanta, participating in their first European final following a memorable run that included a stunning quarter-final elimination of Liverpool.
Ahead of the first of 2023-24's European finals, here's the key storylines and Opta facts surrounding the two contenders.
One down, two to go
Wednesday's game offers Bayer the chance to complete the second leg of an unbeaten treble.
On Saturday, they became the first team in Bundesliga history to enjoy an unbeaten season, while only Arsenal (in 2003-04) and Juventus (2011-12) had previously achieved the feat in Europe's top five leagues this century.
Leverkusen are still unbeaten in 51 games in all competitions this season (42 wins, nine draws), with 12 of those coming in the Europa League (nine wins, three draws).
Three sides have previously won the competition without losing a game, with each of those triumphs coming within the last five editions – Chelsea in 2018-19, Villarreal in 2020-21 and Eintracht Frankfurt in 2021-22.
Wednesday's match will be the third major European final in Leverkusen's history, with Bayer beating Espanyol in a two-legged UEFA Cup final in 1988 and losing 2-1 to a Zinedine Zidane-inspired Real Madrid in the 2002 Champions League showpiece.
Alonso has taken Germany and Europe by storm with his brand of progressive, possession-based football, and Bayer's total of 6,622 successful passes in the Europa League this season is the most by any team in a single edition since 2019-20 victors Sevilla recorded 6,971.
Their passing accuracy of 89.5 per cent is the second highest on record (behind Nice in 2017-18, 90 per cent), while their 94.3 per cent success rate with short passes is the best ever recorded in a Europa League campaign.
But even when Leverkusen have been less than free-flowing, they have found ways to avoid defeat.
They squandered a 2-0 first-leg lead in the second leg of their semi-final tie against Roma, only to fight back for a 2-2 draw which saw them progress 4-2 on aggregate. Josip Stanisic scored a 97th-minute equaliser in that game, the sixth goal Bayer have scored in the 90th minute or later in the Europa League this term.
That is the most ever managed by a team in a single major European campaign, and they also rescued their unbeaten Bundesliga record with last-gasp strikes against Borussia Dortmund and Stuttgart last month.
If Leverkusen find themselves with their backs against the wall on Wednesday, viewers would be wise not to rule them out.
Can the nearly men get over the line?
Leverkusen's Bundesliga triumph has allowed them to shake off their "nearly men" tag, but Atalanta are hoping it's a case of fourth time lucky for them in major finals under Gian Piero Gasperini.
La Dea, whose only major trophy win came in the Coppa Italia in 1962-63, were beaten 1-0 by Juventus in the Coppa Italia final last week – their third loss in that competition's showpiece game under Gasperini.
However, they bounced back with a 2-0 Serie A win over Lecce on Saturday, Gianluca Scamacca and Charles De Ketelaere scoring as they secured a top-five finish and Champions League qualification for 2024-25.
A return to Europe's premier club competition is just reward for a fine campaign for the Bergamo club, who will finish a Serie A season with more than 65 points (currently 66) for the fifth time (with all seasons adjusted for three points per win).
The four previous instances – in 2016-17 (72), 2018-19 (69), 2019-20 (78) and 2020-21 (78) – also all came under Gasperini.
While their free-flowing attacking play has returned this campaign, La Dea have also been excellent without the ball, facing just 2.8 shots on target per Europa League game on average. That is the lowest rate of any team in the 2023-24 competition, with opponents Bayer facing 4.1 per match.
Their backline can expect to be tested on Wednesday, though, with Bayer's total of 232 shots in the Europa League this season the most by any team in a single edition since Chelsea tallied 247 in 2018-19.
The coaches
Fans can expect an intriguing tactical battle between two progressive coaches at the Aviva Stadium.
Gasperini has overseen the most successful period in Atalanta's history since taking charge in 2016, though this will be his first European final as a manager.
At the age of 66 years and 117 days, he will become the oldest coach to take charge of his first major European final, and the oldest overall since Jupp Heynckes led Bayern Munich to glory in the 2013 Champions League final (68 years, 16 days).
His counterpart Alonso – at the age of 42 years and 179 days – will be the youngest coach to manage a men's European final since Roberto Di Matteo oversaw Chelsea's memorable victory in the 2012 Champions League final at the age of 41 years and 356 days, beating Heynckes' Bayern.
Having played for Liverpool in the 2005 and 2007 Champions League finals, Alonso will also become just the fourth person to play in and manage in a major European final this century.
Zidane played for Madrid in the 2002 Champions League final then managed them in the 2016, 2017 and 2018 editions. Antonio Conte played for Juventus in the 2003 Champions League showpiece and coached Inter for the 2020 Europa League final, while Giovanni van Bronckhorst achieved the feat as a Barcelona player (2006 Champions League) and Rangers boss (2022 Europa League).
Players to watch
The likes of Alejandro Grimaldo, Victor Boniface, Granit Xhaka and Robert Andrich have played crucial roles for Bayer this season, but their key man is undoubtedly Florian Wirtz, who was named Bundesliga Player of the Year on Monday.
Wirtz scored 11 goals and provided 11 assists throughout Bayer's triumphant Bundesliga campaign, also recording eight goal involvements (four goals, four assists) in the Europa League this term – the most of any Leverkusen player.
Meanwhile, his total of 28 open-play chances created in the 2023-24 competition has only previously been bettered by five players in a single edition, most recently Amin Younes for Ajax in 2016-17 (30).
For Atalanta, all eyes will be on Scamacca, who scored outstanding goals against Liverpool and Marseille in the last two rounds.
The former West Ham striker has six goals in the Europa League this season, a tally only previously bettered by two Italian players in a single edition. Giuseppe Rossi netted 10 times for Villarreal in the 2010-11 tournament, while Ciro Immobile scored eight for Lazio in 2017-18.
Prediction
Leverkusen enter Wednesday's game as favourites, with the Opta supercomputer rating their chances of victory within 90 minutes at 50.2 per cent.
Atalanta, however, should not be ruled out, having won seven of their nine matches since losing 1-0 in the second leg of their Europa League quarter-final tie against Liverpool (one draw, one defeat).
They are assigned a 24.4 per cent chance of victory, with 25.4 per cent of the supercomputer's match simulations finishing level, which would mean extra time and potentially penalties.