Valverde produced a superb display, punishing City's defensive lapses to hand the Spanish giants a 3-0 advantage heading into the second leg.

Real were without injured trio Kylian Mbappe, Jude Bellingham and Rodrygo, but still struck decisively. City began brightly before the game unravelled after 20 minutes when Thibaut Courtois' long pass sent Valverde through to round Gianluigi Donnarumma and score.

The Uruguayan doubled the lead seven minutes later with a low finish and completed his hat-trick with a brilliant volley after an inventive touch past Marc Guehi.

Real could have extended their lead when Donnarumma fouled Vinicius, but the goalkeeper redeemed himself by saving Valverde's penalty.

City had chances of their own, with Courtois producing a fine leg save after Nico O'Reilly dispossessed Thiago. Guardiola's side created opportunities but were exposed defensively as Real repeatedly found space.

The defeat leaves City needing a major comeback to stay in the competition, though their chances created may offer some hope ahead of the second leg.

Real Madrid manager Alvaro Arbeloa praised both his team's discipline and Valverde's performance.

"This was the match where we stuck to our plan the most. We were a true team," he said. "I'm very happy for Valverde. He's the Juanito of the 21st century; he perfectly embodies what Real Madrid is all about. The night he had tonight fills me with pride. It's a reward for so much sacrifice."

Arbeloa also rejected any suggestion his side had been underestimated.

"Better than you expected, right? I'm very happy for how much the Bernabéu and the players enjoyed it. They deserve it, for all the suffering and hard work. It's clear that the feeling from outside wasn't one of great confidence in this team. We've shown that we are Real Madrid; we should never count ourselves out."

Guardiola admitted the task facing City in the return leg will be steep.

"Right now, not much," he said when asked about his side's comeback chances. "Of course we're going to try and it is difficult right now. But we will be there with our people and we will do better to be more active in the final third and we will try."

The City manager also pointed to defensive lapses and Madrid's ability to break quickly. "It's difficult sometimes to control transitions when we lose the ball and they connect. The first goal was not well defended and then after that the quality they have."

Giorgi Mamardashvili could be joined by compatriot Khvicha Kvaratskhelia at Liverpool