Spanish full-back Carvajal was given a torrid time by Jack Grealish and said after the final whistle that Real allowed their opponents to dominate them, before insisting that the 14-time winners will use the defeat as motivation for another challenge next year.
“We can recognise that City were better, we were lacking something,” he stated.
“It wasn't attitude we were lacking but we allowed ourselves to be pressed back too much. In the second half, we had our best moments.
“We knew that City were very strong at home but after the first leg we were left with the feeling that we could be better than this here – better on the ball.
“We are Madrid; we'll come back stronger and we'll work really hard next season to be back at this stage of the tournament.”