Despite guiding Chelsea to the Premier League title in his first season at Stamford Bridge, Conte has been repeatedly questioned over his future in recent months, amid continued speculation he could depart before his contract expires in June 2019.
Leicester had to play the final 22 minutes with 10 men after Ben Chilwell was sent off for two bookings, and their manager Claude Puel felt the incident had denied his side a chance of taking the three points.
Chelsea have now been involved in three consecutive 0-0 draws in all competitions for the first time in the club's history.
James Ward-Prowse had scored twice in the first half before Andre Gray pulled one back and Saints were crestfallen when Doucoure's equaliser was allowed to stand having stooped to nod into the net, although the ball missed his head and he swept it home with his arm.
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A segunda mão do dérbi de Londres, desta feita no estádio Emirates, casa dos " gunners ", está marcada para 24 de Janeiro. Chelsea e Arsenal disputam uma das vagas na Copa da Liga Inglesa nesta quarta-feira, às 18h (de Brasília).
"We didn't play well but that's when we need the fans behind us".
But misplaced passes and lapses of concentration littered Chelsea's play.
Asked for his thoughts on Leicester's Jamie Vardy, Conte said: "For sure Vardy is a really good player and I don't like to speak about players of other teams but in this case we are not talking about transfer market".
The Foxes had more attempts on goal than their hosts, who were restricted to counter attacks all through the first half until the introduction of Pedro Rodriguez and Willian in the second half.
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"But we knew we were playing against a good opponent, maybe the worst opponent we could have played in this moment". But it's something that we are thinking about a loan until the end of the season.
"I have a lot of experience to deal with this type of situation".
"The most important thing is that I am happy". We tried to win the game.
On Friday, Mourinho said he wanted an end to the story despite still harbouring ill-feeling towards Conte, who appears content to close the chapter.
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