Barca thrashed Seville-based Betis 5-0 in last week's first leg at the Nou Camp and coach Pep Guardiola rested several first-choice players, including World Cup-winners David Villa, Sergio Busquets and Pedro, for the return which they lost 3-1.
The 2009 winners were reeling when Jorge Molina netted twice in the first seven minutes before World Player of the Year Lionel Messi, who had been largely anonymous until then, scored a trademark breakaway goal in the 38th.
Betis midfielder Arzu hooked the ball into the net on the stroke of halftime to revive the home side's slim hopes and they were further lifted when Messi scuffed a penalty over the crossbar shortly after the break.
Despite their elimination, the home fans, who have seen their financially-troubled club slide into administration, were relishing their moment back in the limelight and enjoying their team's performance, which suggested they will be worthy opponents if they seal promotion this season.
"Being from the second division it was a privilege to play against Barcelona," Molina said in a television interview.
"The idea was to make the most of it and I think the supporters enjoyed it tonight and we did too," he added.
"We have to separate ourselves from (the financial problems) and focus on achieving our goal of getting back into the first division."
The Andalusian club, who are bottom of La Liga, won last week's first leg 1-0 at home and built on Sunday's gritty 1-1 draw at home to Real Madrid in the league to beat the Galicians 3-2 on the night for a 4-2 aggregate success.
Holders Sevilla led the charge into the last four on Tuesday when Renato's early strike set them on their way to a 3-0 win at home to Villarreal and a 6-3 aggregate success.
Real Madrid or their city rivals Atletico await in the semi-finals, with Real holding a 3-1 advantage from the first leg at their Bernabeu stadium ahead of Thursday's return match across town at the Calderon.
