The match at the Santiago Bernabeu was marked by the captain of the "Kings", Federico Valverde, who scored a hat-trick in just twenty minutes.
After the match, City coach Pep Guardiola admitted that his team's chances of reaching the quarter-finals are not great at the moment, but he said that his team will not give up.
"At the moment - not much," said Guardiola when asked about the chances of progressing.
"We will try, even though it is very difficult now. In our stadium, with the support of the fans, we have to be more active in the final and try," said the Spanish expert.
The Citizens could have been four goals down, but Gianluigi Donnarumma saved Vinicius' penalty in the second half.
"3:0 is still better than 4:0, we can't deny that," said Guardiola.
The Spanish expert believes that his team did not play badly, but that a concrete finish was missing.
"I think we tried to do our best, but we didn't create chances where Courtois had to intervene more seriously. We got to the penalty area often, but we lacked that finishing touch," the City coach pointed out.
The second leg is next Tuesday at the Etihad. The winner of this two-legged tie will almost certainly advance to the quarterfinals against Bayern Munich, who defeated Nikola Krstović's Atalanta (6:1) in the first leg in Bergamo.
