The Blancos director and club legend was proud of the side's efforts, despite a failure to reach the Champions League final for the 11th year in a row
Despite a 2-0 victory on the night, a 4-3 loss on aggregate meant it was Jurgen Klopp's side who qualified for the showcase event at Wembley on May 25, but Butragueno was proud of the team's battling spirit.
"The team has given their best shot and fought to the end. It was a shame, but the players should not feel disappointed. We appreciate all the effort they have given to the fans," the 49-year-old told the club's official website.
"The first 15 minutes were crucial in the tie. We had three clear chances, one-on-one with the goalkeeper, and we did not manage to score any.
"In these games there is always an important psychological effect. If we had scored a goal early on everything would have changed.
"We are proud of our players for the effort they have made and appreciate all the support given to us by the public. The players have responded wonderfully and have fallen just short of the major event."
Having been dumped out of the Champions League and with La Liga all-but-mathematically impossible to win this season, Butragueno has set his sights on the Blancos winning silverware in the Copa del Rey.
"We must now fight to win the Copa del Rey, it is our duty," he concluded.
Madrid face local rivals Atletico Madrid in the final at Santiago Bernabeu on May 17.