The result confirmed a 5-1 aggregate loss for Carlo Ancelotti's side in the quarter-finals.
Vazquez was a surprise inclusion in the starting line-up for the second leg at the Santiago Bernabeu, and after the match, he shared a candid assessment.
"It was a difficult game, we didn't have all the chances we would have liked," he said, according to Marca.
"We didn't lose face in the game but there were many interruptions and the balance didn't fall on our side and we couldn't do what we wanted.
"We lacked more clarity with the ball, and also some patience when it came to carrying the ball from side to side to penetrate a defence that was very organised.
"They came to defend, in the first half they didn't do anything and in the second with the team turned over they found success."
Vazquez's current contract expires at the end of the season, and he seems unlikely to receive a new deal.
He added: "Just like when we win, we are all responsible when we lose too. It's part of football, Real Madrid knows that we always give our all, it can go well or badly, we always stand up for ourselves.
"We will come back stronger. Real Madrid will always come back and thank you for everything."
Real Madrid have reportedly struck a strategic deal with Arsenal, securing priority access to star defender William Saliba should the Gunners ever decide to sell him before his contract expires in 2027.
Bayer Leverkusen head coach Xabi Alonso has chosen not to comment on growing speculation linking him with a potential return to Real Madrid for next season, insisting that now is not the appropriate time to discuss his future.
Arsenal manager Mikel Arteta has expressed confidence that forward Kai Havertz could make a surprise return from injury before the end of the season, raising hopes that the German international may be available for their UEFA Champions League push.
Arsenal have reportedly cooled their pursuit of Wolverhampton Wanderers' forward Matheus Cunha due to concerns over his on-pitch behaviour, according to recent reports.
