Chelsea’s defeat, their first in eight league games, left them 11 points adrift of leaders Manchester City, who visit second-placed Manchester United in Sunday’s Manchester derby.
“We have to consider that this is the fourth game we’ve lost in 16 games,” Conte told Sky Sports at the London Stadium.
“In my previous experience, it won’t be possible to fight for the title. With four defeats in 16 games, we must have another target.”
Elsewhere, Tottenham Hotspur ended a run of four games without victory with a thumping 5-1 home win over Stoke City at Wembley in which Harry Kane scored twice.
Having previously been beaten by Burnley, Manchester City and Crystal Palace, Chelsea have lost just one fewer game than in the entirety of their triumphant 2016-17 campaign.
Austria international Arnautovic struck in the sixth minute, neatly exchanging passes with Manuel Lanzini and cutting inside Cesar Azpilicueta before curling a low shot past Thibaut Courtois.
It was West Ham’s first win in nine league games and confirmed the progress they have made under new manager David Moyes, who saw his side narrowly beaten 2-1 at Manchester City last weekend.
“The win, the spirit of the team, how they stuck together and more importantly a lot of the basics were done well today,” said Moyes. “All that really pleased me.”
West Ham remain in the relegation zone, but they are now level on points with fourth-bottom West Bromwich Albion, who lost 1-0 at Swansea City in Alan Pardew’s second game as manager.
Wilfried Bony scored for the second game running to lift Swansea off the foot of the table.
Spurs claimed a fourth successive four-goal win over Stoke, making Mauricio Pochettino’s side the first team to have won by four goals in four consecutive English top-flight meetings with the same opponents.
Son Heung-Min’s cross was deflected in via Stoke defenders Kurt Zouma and Ryan Shawcross to put Spurs ahead and Son made it 2-0 by rattling in a pass from Dele Alli in the 53rd minute.
BENTEKE BLOWS IT
Kane’s two goals – a header from a Ben Davies cross and a left-foot curler – took his tally for the season to 18 in all competitions and Christian Eriksen completed the rout.
Spurs moved above Arsenal into fifth place on goal difference ahead of their local rivals’ trip to Southampton on Sunday while Stoke, who replied through Shawcross, have now lost 1 000 top-flight games.
“That is how we need to play from now,” said Spurs manager Pochettino.
“Consistency between now and the end of the season is so important if we want to finish in the top four. The team showed their true quality.”
Burnley are level on points with the two north London heavyweights after Scott Arfield scored in a 1-0 home win over Watford, who had Marvin Zeegelaar sent off for a studs-up foul on Steven Defour.
Crystal Palace fell to the foot of the table after Belgian striker Christian Benteke squandered a stoppage-time penalty in a 2-2 draw at home to Bournemouth.
Jermain Defoe put Bournemouth in front and then equalised with a brilliant dipping volley after Luka Milivojevic’s penalty and a close-range effort by substitute Scott Dann had put Palace in charge.
Palace were awarded a last-gasp penalty when Charlie Daniels felled Wilfried Zaha, but Benteke’s tame effort was repelled by visiting goalkeeper Asmir Begovic.
Palace manager Roy Hodgson said Benteke had made a “unilateral decision” to take the penalty, ignoring his instructions.
Steve Mounie’s first goals since the opening day earned Huddersfield Town a 2-0 win over fellow promoted team Brighton and Hove Albion as David Wagner’s side snapped a four-game losing streak.
In-form Leicester City visit Newcastle United in the day’s late game.