The away fans played a key role as Frankfurt raced into a three-goal lead before Barcelona brought respectability to the scoreline with two stoppage time goals of their own.
Frankfurt's 3-2 win at the Camp Nou saw them progress to the semi-finals 4-3 on aggregate and they will meet West Ham United in the next round.
Per UEFA regulations, Frankfurt were entitled to 5000 tickets but more than five times that number cheered the German side to an unlikely victory.
"What has happened in the stands is a shame that cannot be repeated, we must process information and we have to take action, but it is unfortunate," Laporta told Mundo Deportivo.
"We will have to be stricter and not allow certain things, I feel ashamed as a Barcelona fan. I feel embarrassed with what I saw in the stands, I apologise.
"It was very serious. We are processing all the information, and we will give explanations. What happened today is not usual and should not have happened."
Barcelona will now likely finish the season without a trophy as they have been knocked out of the Cops del Rey and are 12 points behind Real Madrid in the La Liga title race.
