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The Blues defeated Palmeiras 2-1 on Saturday to become champions of the world for the first time in their history.
Burley slammed his former club for treating the competition with respect live on-air and took aim at goalscorers Romelu Lukaku and Kai Havertz.
He said: "I don't even watch this competition I think it's a nonsense. They're off salivating about winning it. You've got Romelu Lukaku scoring a good header, you've got Kai Havertz scoring a penalty... do it when it matters!"
"As they're off celebrating like they've won the World Cup, Manchester City are racking up a 16 point lead on Chelsea where it really matters: the Premier League. ... I don't buy £100M strikers to win the bloody Club World Cup."— ESPN FC (@ESPNFC) February 13, 2022
- @CraigBurley 🗣 pic.twitter.com/jJd3SllnD0
The former Scotland international quickly realises Havertz scored the only goal of the game in May's Champions League final win over City.
Chelsea's participation in the Club World Cup means Premier League fixtures against Leicester City and Arsenal had to be postponed.
Burley continued: "Alright Havertz scored in the Champions League final. "As they're off celebrating like they've won the World Cup, Manchester City are racking up a 16 point lead on Chelsea where it really matters: the Premier League.
"The big competition for them. They're off celebrating like the Club World Cup is the best thing since sliced bread. Meanwhile, they're getting their backside booted all over the place by City.
"The Club World Cup is a showcase event, a plastic trophy. I don't buy £100 million strikers to win the bloody Club World Cup, I buy them to challenge Manchester City and Liverpool in the Premier League."
Burley's comments have rattled fans on social media, who see the Club World Cup as an exciting competition to be involved in.
Chelsea are only the third English side to win the Club World Cup, after Manchester United in 2008 and Liverpool in 2019.
One commented: "Think about how many games we've had to win to get here."
Another put: "We've already won the Premier League though? Cry more."
While a third said: "So he wanted us to lose it? What’s his point?"
Gilette Soccer Saturday presenter Jeff Stelling echoed Burley's thoughts earlier on Saturday.
Lukaku opened the scoring in the 54th minute after heading home Callum Hudson-Odoi's cross.
Palmeiras equalised from a penalty ten minutes later when Thiago Silva handled the ball inside the area.
Raphael Veiga fired past Edouard Mendy to ensure the game went to extra time.
Chelsea scored a penalty of their own in the second half of extra time through Havertz.
It looked as if captain Cesar Azpilicueta would take the spot kick, but the mind games let Havertz have time to focus.
The 22-year-old sent Weverton the wrong way to secure a historic victory in Abu Dhabi.
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