The Portugal international and team-mate Federico Fazio were proud of their side's efforts, despite suffering a 2-0 defeat in the Uefa Super Cup clash
A couple of goals from Cristiano Ronaldo clinched the trophy for Carlo Ancelotti's side in Cardiff as they comfortably saw off the Europa League holders to win the first continental prize of the season.
Beto was proud of his side's efforts on the night but admits that the strength of Madrid's star-studded line-up was simply too much for Unai Emery's charges.
"I'm proud of what the team did tonight," he told reporters after the match.
"It just wasn't possible to beat the team that have the best players in the world.
"We thought we could win, but we leave here with our heads held high."
Defender Federico Fazio added that both the team and the travelling supporters could take great satisfaction from their efforts in Wales.
"We gave everything to win the Super Cup. The fans saw the desire of the team. It's a source of pride to play for this club," he said.