Falcao scored twice in the first half of Wednesday's final before Brazilian Diego wrapped up Atletico's second Europa League in three seasons late on.
And it was Falcao — who scored the only goal for Porto in last year's final and has now scored 29 goals in the competition in two seasons — that hogged the headlines.
"Falcao is already an Atletico legend" said Madrid sports daily Marca of the 26-year-old who was signed last summer to replace departing stars Diego Forlan and Kun Aguero.
"They call him 'the Tiger' and they do so for a good reason. He tore Athletic apart in a perfect display of finishing and penalty-box prowess," the paper continued.
Leading daily El Pais heaped further praise on Falcao, calling him "the perfect striker" and highlighting that this was the second season running in which he had won the tournament and finished as the competition's leading scorer.
AS — the main capital-based rival to Marca — led with "That's Why We Support Atleti." Years ago, a Spanish television advert featured a small boy asking his father, "why do we support Atleti?" a club known better in recent times for scrapping in the lower reaches of La Liga and struggling to keep up with cross-town rivals Real Madrid.
But AS editor Alfredo Relano paid tribute to a club that, despite experiencing more than its fair share of lows, has now won the Europa League twice in three campaigns.
"This Atleti are strange," he said. "They win the same trophy twice in three seasons with two completely different sets of players (none of the 2010 team started against Athletic).
"Why do we support Atleti? This is why. Because of these rare but different moments of happiness, for that feeling of living on the edge."
There was "no ceiling" to Falcao's ambition after the Colombian's brilliant finishing brought Athletic Bilbao to their knees, Atletico Madrid coach Diego Simeone said.
Atletico, desperate to build a side that can regularly compete in the Champions League alongside Real Madrid and Barcelona, dug deep into their pockets to splash out 40 million euros and bring him from Portugal to the Spanish capital last summer. The 26-year-old has repaid their faith with 12 goals in the Europa League and 23 in La Liga.
Simeone, winning his first European trophy as a coach after securing domestic titles in his homeland Argentina with Estudiantes and River Plate, admitted Falcao's talent and ambition could tempt bigger clubs.
"I'll have to hold on to him won't I," a drained-looking Simeone told a news conference, offering the hint of a smile.
"I have known Radamel since he was very young, we were champions in Argentina (with River Plate) and we are champions again today.
"I'm very fond of him, he's an admirable player, he always wants more and I believe there is no ceiling to his ambition.
"I hope he will stay with us at Atletico Madrid and if not I'll be happy with whatever is best for him. I hold him in very high esteem. I love him very much." Simeone also said signing Brazilian Diego, who scored the third goal, on a permanent deal could be key to Atletico's ambitions of progressing. Diego failed to shine at Juventus and Wolfsburg before leaving Germany on a season long loan.
"Radamel and Diego are both determining players. We know we can win a match when they are on the pitch," added Simeone.
"I hope we can also play in the Champions League, let's see if Diego can stay with us." Tenth in La Liga when the former Argentina captain took charge, Atletico have improved to fifth and still could claim a Champions League place if results in the final weekend of the season go their way.
"I feel very proud about my players, very proud of the fans and I'm grateful to the people who trusted in the team and in myself some months back in December so we could reach this target."
