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.
Chelsea must now win at Newcastle on Sunday, and hope Liverpool lose at home to Brighton, to pinch a top-four finish.
"But we must respect Huddersfield".
"This is an unbelievable achievement. We have a further season in the Premier League", Wagner told the BBC. For sure Chelsea were the better team and we had Lady Luck on our side. "We stole a point but we needed it".
"I'm really happy that this very intense period is over now because we have one week to prepare for Brighton - that feels like a year and we will use that".
"We've done it on our own, we didn't rely on anybody".
"The situation wasn't in our hands before this game and after this draw the possibilities are less than before", Conte said.
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"When you create so many chances you must take them, but in this season it's not the first time we are not clinical". But we weren't able to win the game.
Socceroos star Mooy's long pass sent Laurent Depoitre racing through on goal, the striker getting to the ball ahead of the sluggish Caballero and regaining his composure to slot into the open goal. "We had great performances individually but it's been all about the team". But we must accept the result.
Huddersfield also grabbed a point from runaway champions Manchester City last week.
Asked how he planned to celebrate with the squad, Wagner replied: "The guys just said we cancelled their flight".
Spurs capitalised on Chelsea's slip-up to ensure they will have Champions League football for a third consecutive campaign when they move into a new 62,000 capacity stadium next season.
Conte's men began with objective and a degree of fluency despite his decision to make six changes from the team that beat Liverpool, but the visitors' obstinate game plan soon sent the match into a tedious drift, punctuated only by the frequent fury of Stamford Bridge at Lee Mason's officiating.
Marcos Alonso bagged a fortuitous equaliser but the Blues couldn't find a priceless victor. But I'm totally focused on the present.
Their only chance of winning a title this season is now in the English FA Cup where they will meet Manchester United in the final on May 19.
Chelsea threw everything they had at Huddersfield in the closing stages, but somehow the visitors managed to cling on to a priceless point.
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