The Argentinian was pulled up by VAR for lashing out at Asier Villalibre in the final minutes of the additional 30, after Inaki Williams had netted the decisive goal in the fourth.
Antoine Griezmann had opened the scoring for Barcelona in the 40th minute, slotting past Bilbao goalkeeper Unai Simon to give his side the lead, only for Oscar De Marcos to find the leveller just two minutes later.
Barca looked to have secured victory when Griezmann turned home his second goal of the game from seven yards out in the 77th minute, but Bilbao substitute Villalibre volleyed in a 90th-minute equaliser.
Williams curled the ball into the top corner to put Bilbao ahead for the first time in the game, before things went from bad to worse for Ronald Koeman’s side as Messi saw red.
"I understand what he did," said Koeman of Messi's red card. "I don't know how many fouls they committed against him. He tries to dribble and can't."
Koeman revealed Messi insisted he was fit to start the match despite an injury problem and he stressed the defeat was not a major setback to his side as they look to get into contention for bigger prizes this season.
"After so many years, he knows when he can play and when he can’t," Koeman said of Messi. "He decided to play and that’s it. It’s better I don’t speak [about the referee]. I will not give an opinion.
"In the end, this is not a step backwards. A trophy is convenient to show that you’re on the right path, but we’ve still showed that we are.
"We’ve done everything to win, but we were very tired. For many players it will prove a good experience to have played in this final."