Zinedine Zidane's side triumphed 1-0 on aggregate thanks to an own goal from Fernando in the second leg at the Santiago Bernabeu.
City had never reached the last four of the competition but failed to cause Madrid any significant trouble in two very cagey matches, allowing Zidane's men to progress to the final, where they beat Atletico Madrid on penalties.
The defeat still rankles with Pellegrini, who felt that his side failed to take advantage of unconvincing performances from the 11-time European champions.
"I think that we lost against a Madrid who played very poorly in the two games... but we played much worse. We didn't hit the target in the whole tie!" he told Marca.
"If you get knocked out by an exceptional Madrid, okay, but we lost to a Real who didn't do anything and ultimately it was through an own goal. That made me angry."
Pellegrini believes City deserve credit for reaching the last four, however, especially since it had been announced in February 2016 that he would be replaced by Pep Guardiola at the end of the season.
"From then on, the relationship with the players was more complicated," he said. "The authority wasn't the same. When you know that there's going to be a new coach, the atmosphere changes. But even that year, we reached the Champions League semis.
"In the three years at City, we had bad luck in that we played Barca and that semi against Real. But I'm very proud of what was done. It was a very good three-year period.
"We won two EFL Cups and a Premier League, being the top-scoring team in all of those years. The numbers were fantastic."
It was Pellegrini's shock admission in a media conference that he would be leaving at the end of the season that prompted City to announce Guardiola's arrival.
The 63-year-old, now at Hebei China Fortune, admits he would do things differently given another chance but says the constant speculation around his future had begun to affect him.
"If you ask me now if I would have done differently, I'd say yes. I would have waited until the end of the season," he said. "It was my own initiative but I would do it differently. But there were so many rumours... it was making me uncomfortable."
City's win over Bournemouth on Monday took them to second in the Premier League table, although they remain eight points behind leaders Chelsea.
Pellegrini feels that those who predicted a routine title win for Guardiola in his first season in charge have been given something of a wake-up call.
"I think he values my work over those three years a little more," he said. "It's not easy to win the Premier League. Look at Chelsea this year.
"There is a myth that City are the ones with the most money, but now there are five teams who spend a lot.
"Maybe a lot of people thought that, with Pep's arrival, they'd win the league by 15 points. In England, that's not the case."