Henrique, who was named the competition's best player, helped kickstart Flamengo's recovery from a goal down with a fine piece of skill that led to Gabriel Barbosa's 89th-minute equalizer.
"We adopted a phrase that we never lost sight of: 'Fight until the end'," said the Brazil international, who scored five goals and provided five assists in Flamengo's triumphant campaign, reports Xinhua news agency.
"The game only ends when the referee blows the final whistle. We believed in ourselves and didn't give up until the end. There was no way we could leave here without being champions because this team deserves it."
Barbosa, who also struck the winner in the third minute of stoppage time, described the match at Lima's Estadio Monumental as the highlight of his career.
"I'm grateful for this moment that's going to stay with me for the rest of my life," he said. "I'd like to thank my family, the fans and the players. I want to urge everybody to help us celebrate in Rio tomorrow."
Diego Ribas, who helped shift the momentum in Flamengo's favor after coming off the bench in the second half, said he always believed Flamengo were in the match.
"I don't want to say that it was easy, but we believed at halftime that we could win it," the former Atletico Madrid player said. "Even though we were behind, we kept at it and knew that if we played the way we have all year we'd have a chance."
( With inputs from IANS )