However, Chelsea can extend their lead to seven points if they beat struggling Middlesbrough at home on Monday and clinch the title if they defeat West Brom away next Friday.
Mauricio Pochettino is disappointed to see Spurs' title hopes take a massive hit, but he wants his side to finish strong.
Son Heung-Min went closest to breaking the deadlock for Tottenham in the second half but West Ham were always unsafe and Lanzini, wasteful with a first-half chance, delivered what could be knockout blow to Tottenham's title hopes.
West Ham kept Tottenham at arm's length once it went ahead and the final whistle sparked scenes of jubilation around the ground.More news: Over 3 feet of snow falls in Colorado's mountains
Spurs travelled to the London Stadium looking for a 10th straight victory, but instead Manuel Lanzini's strike all but handed the Premier League crown to Chelsea.
After seeing their long pursuit of Leicester last season end in failure, the same thing looks set to happen to Tottenham this season. "I'm very proud. It's so hard sometimes to keep your level". When you are fighting for the title, the goal we conceded, you need to stop before and not concede this type of goal.
"You need to do more, to push to your limit, and unfortunately we were not capable of doing that".
"We should have increased our level, but we didn't do it".More news: U.S. military conducts airstrike on pro-government forces in Syria
"We shouldn't forget what we've done until now", he added. "When we conceded it was so hard to come back in the game".
Christian Eriksen, usually so composed, betrayed the anxiety creeping into Tottenham's play when he let Son Heung-Min's pass deflect harmlessly towards Adrian when a sight of goal came his way inside the West Ham area.
"Spurs are a top team, I think they'll be the team to beat in a few years".
The only teams that could mathematically catch Spurs (77 points) for second place are Liverpool (69) and Manchester City (66) - the latter have a game in hand - but it is extremely unlikely.More news: USA summons Turkey envoy for embassy brawl
Pochettino admitted Spurs lacked the intensity they had shown in recent games, but rubbished suggestions that the pressure had got to his players.
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