Youri Tielemans and Emiliano Buendia struck late in the first half as Villa took control at Besiktas Stadium, with Morgan Rogers adding a third after the break to seal a comfortable victory.
“Right now, there is no happiness. We lost a final. That hurts,” Schuster told reporters. “I said before the game we believed we could win. For 40 minutes we did well, and then it changed.”
Schuster said a well-worked Villa set-piece and a defensive error proved decisive before halftime.
“For the first goal, Villa executed the set-piece well; for the second it was our mistake,” he added.
“At 2-0 down at the break, you see the real character of a team, and the boys did well.”
Despite the defeat, Schuster said Freiburg - who had never previously gone beyond the last 16 in Europe - would, in time, reflect positively on their campaign.
“It didn’t go our way in the end. In a few days we will appreciate what we achieved with our fans, but it is painful right now,” he said.