Bayern Munich took Real Madrid "to the brink of the abyss" in their best Champions League performance for five years, CEO Karl-Heinz Rummenigge has said.
Madrid progressed to the final 4-3 on aggregate after a 2-2 draw at the Bernabeu on Tuesday as Bayern lost in the semifinals for the fourth time since winning the trophy in 2013.
But Rummenigge told the players and departing coach Jupp Heynckes that he would have raised his hat to them had he been wearing one.
"We've seen the best Champions League match that I have experienced with Bayern Munich in the past five years," he said at the club's traditional midnight banquet.
"We all agree that we brought the best team to the brink of the abyss, and Real are currently leading the UEFA ranking. On Labour Day we played with hard work, fighting spirit, unbelievable passion and also courage.
"The only downside is that we failed to push them into the abyss. We drew 2-2. You did a fantastic job. That was the best ad for football.
"I believe not only Bayern, but all of Germany, all of the footballing world, will pay this team and our coach Jupp Heynckes the biggest respect."
Heynckes was appointed as interim coach in October with Bayern struggling, and Rummenigge said he and the team had achieved a lot this season.
"We won the league with a 20-plus points margin. We were the only German club in the Champions League knockout stages," he added.
"Sadly I don't wear a hat but, if I wore one, I'd raise my hat to this team now."
Meanwhile, Corentin Tolisso voiced his frustration at failing to reach the final in Kiev.
"It's the biggest disappointment of my career, even if I had already lost in the semifinals in the Europa League with Lyon last season," the France midfielder told L'Equipe. "It's very tough.
"We stood up and were counted in both legs of the tie, which was decided on small details. We gave everything -- we really wanted to win here.
"We played really well in the first half, throughout the game in fact. There were chances that we should have put away."
Bayern's season comes to an end after the German Cup final against Eintracht Frankfurt later this month.
"We're all very disappointed this evening, but we have to keep going forward, focus on the next game, the next goal," Tolisso said. "We want to win the German Cup."