A 3-0 win at the Bernabeu on Wednesday (Thursday AEDT) put Madrid in control of this round-of-16 tie at the halfway mark after a stunning first-half hat trick by Federico Valverde.
The Uruguay international took on the responsibility of inspiring the record 15-time champions in the absence of injured stars Kylian Mbappe, Jude Bellingham and Rodrygo.
Madrid's victory could have been even more commanding, but Vinicius Junior's casually-taken second-half penalty was saved by Gianluigi Donnarumma.
It will still take a massive turnaround to see City advance after being outclassed by Madrid.
Valverde's hat-trick featured three outstanding goals. The pick of the lot was his third when he flicked the ball over the head of City defender Marc Guehi before volleying home.
City manager Pep Guardiola will likely be worrying that history is set to repeat itself after his team were eliminated at the hands of Madrid in each of the past two seasons.
Defending champions Paris Saint-Germain thrashed Chelsea 5-2, and tiny Bodo/Glimt are also in sight of the quarter-finals after a 3-0 win over Sporting Lisbon.
In Germany, Kai Havertz returned to haunt Bayer Leverkusen and seal a late 1-1 draw for Arsenal.
The Germany international struck an 89th-minute penalty against the team where he started his career and levelled the round-of-16 first leg tie at BayArena.
"I know the stadium well and have taken many penalties from this spot," said Havertz, who left Leverkusen for Chelsea in 2020 in a deal worth $US95 million.
Premier League-leading Arsenal fell behind on Robert Andrich's goal just after halftime.Â
However, Malik Tillman fouled Noni Madueke in the box, and Havertz fired low past Janis Blaswich from the spot.
After dominating the league phase of this year's tournament, English Premier League teams were brought down to earth in the round of 16.
City, Chelsea and Tottenham all fell to heavy defeats, and Liverpool also lost to Galatasaray.
None of England's six teams in the knockouts won their first leg, with Arsenal and Newcastle both picking up draws.
Arsenal will be favoured to overcome Leverkusen at home, and Liverpool only have to overturn a 1-0 deficit in their second leg at Anfield.
But City, Chelsea and Tottenham all face big deficits, while Newcastle travel to Camp Nou to play Barcelona.
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