Kane, searching for his hat trick, saw his effort from a free kick crash off the bar.
"It's such a busy schedule that we have because we play every two or three days and then all are away for the worldwide break so it's impossible".
But two acts of foolishness, alongside many other questionable decisions, by Ivorian full-back Aurier saw him dismissed and gave West Ham a glimmer of hope.
Michail Antonio's first half injury in the 28th minute was the turning point in the contest, as West Ham were the better side up to that point.
However, Spurs hung on to claim all three points in the London derby.
Having threatened the chief coach with a loss of the place at the helm of the team, Slaven Bilic must be very deliberately approaching the choice of both the basic composition and the game plan.
Mauricio Pochettino is the Premier League manager working farthest from his birthplace, but the Tottenham boss knows where to find home comforts in London. Not only that, they were largely toothless in attack, forced to go direct which Spurs on the whole dealt with comfortably.
Tottenham have to be ready for that, they have to be up for the battle. The on-loan Everton man was the only Bolton player to even attempt to run at the West Ham defence and, despite lacking a telling final ball, actually tried to make something happen. There were flashes of real talent against West Ham, but there were also a string of silly fouls in the first half that made a yellow nearly inevitable in the second half. "I prefer to play at Wembley, but it's true the results there from the start of the season have not been the best".
In our preview, we are backing Spurs star Dele Alli as our prediction, and he is available at the best odds of 28/17 at Unibet.
Spurs are looking to win their opening three away games in a league season for the first time since 1991-92.
Chelsea's record signing Alvaro Morata showed he may be worth every penny with a hat-trick in the champions' 4-0 away win over Stoke.
The England striker added: "Obviously I see stuff going round on social media but I don't really think about stuff like that too much, I want to score against every team I play against".
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