England ground out a 3-1 victory over Hungary in a World Cup warm-up on Tuesday
The defeat foiled Chelsea's bid for the league-Cup double.
The Spanish champions went through on 3-2 aggregate after the second leg pre-quarter-final ended 1-1. Juventus and Villarreal also made it to the quarter-finals.
Chelsea romped to a 4-1 home win over Everton in their FA Cup fourth round
Arsenal ended a run of three league defeats by winning 1-0 at Charlton Athletic to climb to sixth 20 points adrift of Chelsea.
Everton's Premier League relegation fears deepened considerably as they collapsed to a 5-0 defeat at Tottenham Hotspur with Harry Kane scoring twice for the rampant hosts on Monday.
John Terry came to Chelsea's rescue on Wednesday when he powered home a 77th-minute header to secure a 1-0 home win over a dogged AS Roma.
The champions beat Aston Villa 2-1 while Manchester United went down 1-2 at home to Blackburn Rovers in the Premier League.
Chelsea and AC Milan drew 1-1 in a friendly match on Sunday as they wrapped up their pre-season tour of the United States.
The English champions-elect, 4-2 up from the first leg, went through 6-5 on aggregate in the Champions League.
An 85th minute goal from a free kick by Ireland winger Damien Duff gave Chelsea a 2-1 victory over Manchester United.
"He has still got a lot to learn, he has to improve when he is part of a defensive organisation," the Chelsea coach said.
It rallied from a 2-0 deficit to draw 2-2 with Chelsea and reach the Champions League final 5-3 on aggregate.
"When you see world-recognised figures like Juergen Klopp and Pep Guardiola behaving like that, it is then replicated by people in youth football and perpetuates the idea that it is OK to do it," Ref Support UK CEO Martin Cassidy said.
Newly-formed New York City FC will begin their preparations for their Major League Soccer (MLS) debut with two friendly matches in Manchester next month, Manchester City said on Tuesday.
Thomas Tuchel arrived at Stamford Bridge in January on an initial 18-month deal with the possibility of an extension, which was granted six days after he led Chelsea to Champions League glory.
Klopp's side won the Champions League, Super Cup and Club World Cup titles last year, but the German said that their rivals will look to close the gap.
Luton pulled one back on the half-hour mark when Chelsea keeper Kepa Arrizabalaga failed to keep out Jordan Clark's low effort which squeezed between his hand and leg into the net.
IMAGES from the English Premier League matches played on Tuesday.
A tap-in by Karim Benzema and a powerful strike by substitute Marco Asensio earned European champions Real Madrid a 2-0 win over 10-man Chelsea.
Jermain Defoe's childhood obsession with scoring goals has put him within reach of a top-five spot in the Premier League's all-time list
Rafael Nadal's dominance on the red claycourts in Paris is unmatched, the Spaniard picking up his 13th French Open trophy last year to match Roger Federer's 20 Grand Slam singles titles.
Chelsea confirmed on its website that they had parted company with the German coach
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Here is a look at the clubs most likely to give City a run for their money next season.
Cody Gakpo scored his first goal for the club as they halted a dismal run
As the United Kingdom now has 19 confirmed cases of coronavirus, Newcastle players and staff have been advised to avoid handshakes in a bid to prevent spreading coronavirus.