The Blues had the chance to overtake Manchester United and Liverpool into second place as the Red Devils were beaten by Tottenham Hotspur at Wembley.
But Chelsea were shocked by Bournemouth at Stamford Bridge, playing with no recognised striker following the loan of Michy Batshuayi, and dropped to fourth on goal difference.
This is now the third time Chelsea have lost 3-0 at Stamford bridge during the Roman Abramovich era:
16 April 2016 vs. Man City
14 November 2010 vs. Sunderland
31 January 2018 vs. Bournemouth
Their highest ever loss. pic.twitter.com/yiBxe0WfSX
— Squawka Football (@Squawka) January 31, 2018
And Conte, reports the Telegraph, admitted his side will have a hard task to keep their place in the top four.
“We must be worried,” Conte told reporters after the game.
“It won’t be easy and we must be prepared to fight and ready to do this.
“I am ready and I think the players are starting to understand that this season, we have to struggle for a position in the Champions League. They know the danger and they understand our situation.
“Their commitment and their behaviour is great and if they hadn’t done that, our place in the table would be worse. If we want to dream I can tell you now we can fight to win the title this season.
“But it is important to look at the reality and know that if we reach a place in the Champions League it will be a great success for us.”
Callum Wilson, Junior Stanislas and Nathan Ake scored for Bournemouth in a 16-minute spell during the second-half as Eden Hazard struggled in a central role in the absence of Alvaro Morata.
Conte’s January blues
In the nine games Chelsea played during the month of January, Conte’s men won just two games (drawing five and losing two).
The Blues started the year with a 2-2 draw against the Gunners in the Premier League and followed that up with three 0-0 draws in three competitions.
The first came in the FA Cup away to Championship Norwich City, then another draw with Arsenal in the Carabao Cup semi-final first leg, before also tieing with Leicester City in the Premier League.
Chelsea once again struggled to break down Norwich in the FA Cup third round replay, conceding an injury-time equaliser after having taken the lead, before edging the game on penalties.
Wins in the league against Brighton and Hove Albion and Newcastle in the FA Cup came either side of a Carabao Cup defeat to Arsenal, losing 2-1 to go out at the semi-finals.
And the 3-0 shock defeat at the hands of Bournemouth on Wednesday night brought the fourth time the Blues have failed to score this year.
Chelsea’s next game in the Premier League is against Watford at Vicarage Road on Monday night.