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.
Per UEFA regulations, Frankfurt were entitled to 5000 tickets but more than five times that number cheered the German side to an unlikely victory.
Barcelona president Joan Laporta promised an investigation into the invasion.
A statement from the supporters'group read: “Last Thursday we experienced a day that will be marked forever as the greatest infamy at our home.
"As fans and members of FC Barcelona we have experienced many victories and many defeats on the field of play, but as a fan group, we have experienced a social humiliation that we will never forget."
The statement continued: "It is difficult for us to understand how an invasion announced for weeks has gone unnoticed by the security department. We wonder if they have been caught by surprise or if inaction has been promoted to get €3million at the box office.
"Nor has it been a surprise that they have paid special attention to the Barca fans and have denied the appearance of more than 30,000 German fans.
"We have to give thanks that given the seriousness of the events, the Eintracht fans are not one of the most conflictive in Europe. Who knows where we would be right now with another group of fans.
"Our task is simple but very complicated, to set the mood and help cheer up the rest of the stadium to get victories, because we are very clear that as fans we are the 12th team player.
"However, the events that took place on Thursday meant that we were forced to take action, as we did during the match and on other occasions, and that is precisely why we will not attend the next match between Barcelona and Cadiz.
“We are convinced that, as members and fans of FC Barcelona, we cannot ever allow again a remotely similar situation, and we ask the parties involved to remember that not everything in life is a few million, especially if we talk about a club that has as a motto ‘more than a club’."
