Falcao scored twice in the first half at the National stadium in Bucharest, a year on from his exploits in last season's final when his goal was enough to secure Porto the Europa League title.
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 said, 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.
"Sometimes experienced players lose that extra something because they have done it before.
"Falcao is not like that, he forgot what he did last year and now he can live (in) the present."
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."