Falcao hailed the unity within Porto's squad after his 17th European goal of the season fired the Portuguese champions to Europa League glory in Dublin.
The Colombian striker headed the only goal of the game against fellow Portuguese outfit Braga just before half-time as Andre Villas-Boas' side claimed their third trophy of an incredible season.
Having secured the league title without losing a game, they added the Europa League to their Portuguese Super Cup triumph with the Portuguese Cup final to come on Sunday.
And Falcao, who broke the record for the amount of goals scored in the competition, said Porto had "dreamt about this since the beginning of the season".
"My 17 goals were very satisfying but the most important thing is that we won. The key was the unity of the team," he said.
Falcao has been linked with a move away from the club due to his prolific form but says he hopes to play in the Champions League with Porto next season, and may sign a new contract.
"I am just thinking about enjoying this right now and Porto wants me a lot. The truth is I want to be at Porto and enjoy it," Falcao said. "Both sides seem to be available and we will see about that [new contract] during the next year.
"Of course, one day I might play in other leagues, of course there are expectations, but now I want to enjoy this and take Porto to the Champions League next year."
Goalkeeper Helton lifted the trophy on his 33rd birthday and added: "The cup is very heavy. It is a wonderful gift.
"We are very happy for all that we have achieved. I want to dedicate this title to my mother. She underwent surgery this week and for sure she is very happy."
Braga manager Domingos Paciencia, who scored over 100 goals for Porto in his playing career and leaves to coach Sporting Lisbon in the summer, said: "I'm sad, like the players.
"Porto were not as dominant as everyone expected. They scored in the 44th minute after we slipped up. In the second half we tried and it was a pity Mossoro couldn't score."