The Rojiblancos needed an extra-time goal from defender Miranda to end their 25-match winless run against their city neighbor and triumph in the domestic cup competition for the first time in almost two decades.
And their coach was delighted with the commitment made by each and every one of his players on the night and in the wider context of their "incredible" progress since his appointment in December 2011.
"It was an incredible game. We had the luck needed to win the trophy. What these players have been doing for the past year-and-a-half is incredible," Simeone told reporters.
"They finally lost their fear and the hearts of each player combined to win the match, and it was amazing. We were fortunate because in soccer, teams that win have a slice of luck. We believed that we'd win the game.
"What brought us these achievements has been this - you see Diego Costa running 50 meters back, see Koke, [Radamel] Falcao and Gabi all sacrificing themselves for the team.
"I'm speechless. Now we have to think about the next game if we want to keep on developing. That's the only way we know."