Michail Antonio struck with 17 minutes remaining as he met Aaron Cresswell's corner from the left.
Spurs failed to register a shot on target in the second-half, but Nuno was quick to defend their performance.
The Portuguese told Sky Sports: "We were the better team, honestly. I think we controlled the game, we had chances. We had possession. West Ham are a good team but they only created chances on counter-attacks and set-pieces. We played better, but this is football.
"The last pass was there but we need to be more aggressive in our offensive game. We controlled the game. The whole game was under control.
"The table is a reference but doesn't guide us. We have to improve our character as a team, our wish to want to achieve a better team game. We need to work on that."
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