Prices for the May 28 final were revealed on Thursday, with some categories nearly doubling in price in two years.
There are 11,000 tickets on open sale, ranging from 150 to 300 pounds with an administration fee of 26 pounds per pair of tickets.
The two clubs in the final will each receive 25,000 tickets, ranging from 80 to 300 pounds.
"We're shocked; asking fans to pay that sort of money, especially in the current economic climate, is outrageous," Michael Brunskill, a spokesman for the Football Supporters' Federation (FSF), told Reuters on Friday.
"UEFA know that fans will want to go to what for many will be a once-in-a-lifetime event and it's nothing short of profiteering at the fans' expense.
"When UEFA announced they were going to move the final to a Saturday they said one of the reasons was to try to encourage more families to attend but how many families can afford to pay that sort of money? You could have a family holiday for that."
After the ticketing announcement, UEFA's director of competitions Giorgio Marchetti defended the prices, saying they should be viewed in line with prices for the World Cup or European championship final.
"We do not want to squeeze every single penny out of the market. We have to benchmark this event against other comparable events," he said.
"This is the market price. Do you think we would have trouble filling Wembley if the prices were higher? We try to strike a balance between the interest of the supporters and the interest of the event. Why should we price the tickets lower than what we think is a fair level?"
The FSF described the administration fee - far higher than that charged for other matches or concerts at the stadium - as "the cherry on a particularly disgusting cake".
"There is absolutely no way of justifying such a high fee and UEFA should be ashamed of themselves," said FSF chairman Malcolm Clarke.
