They came closest in an almighty penalty box scramble in which Andreas Christensen's header was tipped onto the post and a seemingly never-ending wave of blue shots found only heroic red bodies.
"The only way to put on a bit of pressure is (to win)", Conte said.
On a scorching afternoon in the capital it required a great deal of commitment to ensure Chelsea saw the game out, and the players responded by giving their all, with eight of the 11 starters covering over 10 km in the Bank Holiday heat.
Sane's cutback was then turned home by Fernandinho 19 minutes from the end to wrap up the victory, which set two more Premier League records - for most wins (31) and most points (97).
"This season we were predicted as the team to get relegated by miles and I understand it".
We are taking more chances because we are winning, and that's the most important.
Huddersfield have secured their Premier League status with a valiant 1-1 draw at Stamford Bridge, which significantly dented Chelsea's slim top-four hopes.
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The visitors however stunned the home fans when they scored in the 50th minute through Laurent Depoitre who sent Wilfredo Caballero the wrong way. But we must accept the result.
Chelsea coach Antonio Conte is disappointed by how his team's season has played out and criticised the "stupid way" in which they had dropped points after dominating games.
The Blues pressed hard for a victor in a chaotic second half but simply could not find a way past a committed Huddersfield side who will be playing in the top flight again next season.
"We knew it was going to be a tough game, they're very good on the ball so we had to get closer and make it hard, so we did it quite well", Mooy said.
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"We must give compliments to Huddersfield for this result...congratulations to the club".
Chelsea, which plays at Newcastle, is two points behind fourth-place Liverpool, which hosts Brighton.
The Italian, widely tipped to leave Chelsea at the end of the season, sidestepped questions about how to improve his squad, saying he was sure the club would look at that later.
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