The left-back was handed his marching orders late in the second period after picking up his second yellow card, but the Spanish champions are hoping that the decision will be overturned.
"The club have decided to appeal Jordi Alba's red card to the Competition Committee," read a statement on Barca's official website.
"The FC Barcelona left-back was shown his second yellow card on 77 minutes for 'knocking down an opponent in a dispute for the ball', according to Perez Montero's post-match referee report.
"The defender was shown his first yellow card on 51 minutes."
The defeat was Barcelona's first home loss in La Liga for 31 matches.