Roma, trailing 2-0 from the first leg of their round of 16 tie at home, created enough chances at the Bernabeu to have wiped out the deficit before the hour.
Instead, forwards Edin Dzeko and Mohamed Salah repeatedly misfired and two quick goals from Cristiano Ronaldo and James Rodriguez completed a 4-0 aggregate win for the hosts.
Dzeko, in particular, has had an unhappy time at Roma, scoring only eight goals since joining them on a season-long loan from Manchester City in July.
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"There are some matches that go down in footballing history forever and give you a shortcut to success, but you have to try to make them happen," said coach Luciano Spalletti, appearing to appreciate the size of the opportunity which had gone begging.
"The regret is there when you don’t play these matches with conviction and belief – that’s what we were lacking over this tie with Real."
Spalletti, whose side have won their last seven Serie A matches, did not want to hear suggestions that Roma had restored some respectability after avoiding a repeat of the 6-1 defeat to Barcelona in a group match.
That result began the chain of events which led to Rudi Garcia being fired in January, and paving the way for Spalletti to return for a second stint at the club.
Despite reaching the round of 16, Roma managed just one win in their eight-match European campaign, and failed to score in their last three outings.
"When I go into the dressing room after a 2-0 defeat and see the players feeling satisfied because they’re going to be congratulated on their performance, that doesn’t sit right with me," said the shaven-headed coach.
"We should be angry – maybe we’ve not yet realised what a big chance we’ve thrown away over the course of this tie.”
Spalletti pointed out that Real's football was far from irresistible.
"I could congratulate my players on their performance, but that would be living a fairytale and not facing up to reality," he added.
"We’re Roma but we have to play like Roma – we should come to these grounds to show people who we are. We need to improve quickly because it’s not OK. We must do better."
(Writing by Brian Homewood. Editing by Patrick Johnston)
