Mauricio Pochettino admits that a Saturday morning clash with West Ham was a must win game if Tottenham hoped to catch Premier League leaders Chelsea.
Chelsea FC now need just two wins out of the four games remaining in the English Premier League to seal the title for the season.
Tottenham return to Premier League action for the final game at White Hart Lane against Manchester United next Sunday, by which time Chelsea could already be champions.
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.
With Tottenham trailing Chelsea by four points in second place, the challenge now is holding on for its highest finish in 54 years.
Spurs will now find themselves seven points adrift, with only three games to play, if the Blues beat Middlesbrough at home on Monday.
"At this stage of the season it's the same for every team - we're all exhausted physically, mentally".
Dele Alli's follow-up was blocked back to Kane on the edge of the area and the Tottenham striker looked certain to score, yet once again he was denied as Adrian's out-stretched leg deflected it over. "We were not capable of doing more", the goalkeeper said.
"We deserved to win, we did everything", he said.
Spurs aren't mathematically dead yet, but their shock upset loss at West Ham United effectively sealed their fate. But to beat a team like Spurs you need more and we showed quality, especially in the second half.
Had they won for a 10th match in a row they would have moved a point behind Chelsea with three games left. I think it's coincidence. We had the opportunity to reduce the gap but it was not our day.
The visitors were uncharacteristically disjointed and blunt against a well-drilled West Ham side, who had a number of chances at the London Stadium.
After a tepid start, Tottenham should have taken the lead midway through the first half when Harry Kane's 20-yard strike was pushed out by Adrian.