Los Rojiblancos missed out on the European Cup by a matter of seconds to what became an all-conquering Bayern Munich side 40 years ago. Bayern, featuring Franz Beckenbauer and Gerd Mueller, went on to win three European Cups in a row, and yet they almost never won the first, as they went into the final minute of extra time 1-0 down.
The goal had been scored by Atletico's greatest player of all-time, Luis Aragones, just six minutes from the end of extra time, but the Spaniards were denied when Miguel Reina - father of current Napoli goalkeeper Pepe Reina - let Hans-Georg Schwarzenbeck's hopeful effort slip through his grasp. In the days before penalty shoot-outs, Bayern went on to win 4-0 in the replay in Brussels just two days later.
On Sunday an estimated 200,000 Atletico Madrid fans crowded round the Neptuno fountain and surrounding streets in the centre of the Spanish capital to celebrate their side's first La Liga title in 18 years. However, amongst chorus upon chorus of chanting, it wasn't inspirational manager Diego Simeone or top scorer Diego Costa who was the most prominent name, but that of Aragones.
The man who also coached Spain to the first of three successive major tournament victories at the UEFA EURO in 2008, died on 1 February this year aged 75. Since then he has become an inspiration for arguably the most successful season in Atletico's 111-year history.
Homage to Aragones
A picture of Aragones adorned the plane that took the players to the away leg of their Champions League last-16 tie against AC Milan. Once the seven-time European champions had been easily disposed of 5-1 on aggregate, it was one of Aragones' famous decrees "win, win and win again" that met the players in a spectacular display by the Vicente Calderon crowd as they hosted Barcelona in the last eight.
Even after clinching the title with a hard-fought 1-1 draw away to Barcelona on Saturday, Simeone thanked all those at the club who had helped bring about the success. Among that list he included Aragones, who he said "was surely defending in our box during the second half."
Defeat to Bayern in the '74 final was not just heartbreaking. It helped mould a culture of pessimism around the club that was generally sustained despite the odd trophy for the following four decades.
Yet, under the Simeone revolution, the tide is turning within the Spanish capital. Since the Argentine's arrival two and a half years ago, Atletico have won more trophies than Barcelona or Real Madrid.
Far from being the self-confessed "cursed ones", Atletico beat Real in their own backyard to end a 14-year hoodoo in the Madrid derby and win the Copa del Rey final little more than a year ago. The day after Aragones' death, they went top of the league for the first time in 18 years and, despite being briefly knocked off their perch, had the mental fortitude to get back and stay there.
"The capacity to motivate comes from showing them the shirt of this club. The motivation is to play for Atletico Madrid not against whoever is in front us," says Simeone.
However, the chance to not only win their first Champions League title but also continue Real's 12-year wait for their treasured 10th European crown would be the strongest signal yet that the balance of power has tipped to the red and white side of Madrid.
Yet, Atletico's need is also urgent. Any such power shift is likely to be fleeting. The motivation to play for that shirt is complete right now, but unlikely to last long as Europe's big spenders circle to pluck off their best players and possibly Simeone himself.
Saturday's date in Lisbon represents their best shot of European glory for 40 years. Given the harsh financial realities that affect performance at the top level of the Champions League, it could take them 40 years or more to get another chance.