The Blues were always battling against the odds to overturn a 2-0 deficit from the first leg in the Bernabeu and their cause was not helped by a familiar failing as a battling performance was undermined by missing a succession of clear chances.
N’Golo Kante missed a glorious first-half opening while Marc Cucurella was blocked by former Chelsea keeper Thibaut Courtois when he looked certain to reduce Real’s advantage.
The Spanish champions had moments of their own and there are few sides more adept at making opponents pay for wasted opportunities and so it proved.
A lightning counter attack led by Vinicius Junior ended with Rodrygo putting the tie to bed with a close-range finish just before the hour
The Brazilian forward then walked in the second after brilliant, unselfish work by Federico Valverde with 10 minutes left.
Carlo Ancelotti’s quest for an historic fifth win as a coach in this tournament will continue with a semi-final against either Bayern Munich or Manchester City while Chelsea’s interim manager Frank Lampard, who now has four defeats from four games, must somehow lift the grim mood of despair around the club.
