Chelsea succumbed to the Cherries in 16 second-half minutes as Callum Wilson, Junior Stanislas and former Blues defender Nathan Ake all scored to stun the Premier League champions.
The remarkable 3-0 defeat saw the Blues drop to fourth – behind Liverpool on goal difference – and just two points clear of rivals Tottenham following their 2-0 win against Manchester United.
“We must be worried [about finishing in the top four],” Antonio Conte said. “It will not be easy. I am repeating what I have said since the start of the season.
“We have to fight. We must be prepared to fight and we must be ready. I think the players are starting to understand that this season we are going to struggle for a position in the Champions League.
“If we want only to dream and not see the reality, in this case I could tell you we can fight to win the title this season. But it is important to look at the reality and to know that it will be a great success to reach a place in the Champions League.”
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On a hectic transfer deadline day for the Blues, Conte did have one reason to smile with the arrival of Olivier Giroud from Arsenal on an 18-month deal.
Giroud was in the dugout for the Stamford Bridge clash but was unavailable to play after completing his switch too late in the day.
And following Michy Batshuayi’s deadline-day loan switch to Borussia Dortmund, and the absence of the injured Alvaro Morata, Conte was left without a recognised centre-forward – and the Italian admits he is feeling the pressure to get results.
“I think about the pressure and it is normal for a coach and manager,” Conte added. “It is normal if you are Chelsea’s coach.
“We are doing everything and giving 120 per cent, and I am approaching this squad at their maximum level, but if someone does not agree that I am here then you have to accept every situation. I am relaxed about this because I know I am doing a great job.”
On the other hand, Eddie Howe was revelling in Bournemouth’s emphatic win over the champions.
Asked if this was the greatest result of his managerial career, Howe replied: “This is the best because of the performance.
“When we won here at Stamford Bridge in our first season in the Premier League, it was a great moment and an historic night but we were backs to the wall and we rode our luck.
“I don’t think there was any luck connected with today. It is the best performance that we have had at this level and the result has matched it.”