The Croatian played down his side's chances of finishing in the Premier League's top four despite an accomplished win over the title challengers in east London
Michail Antonio's headed goal after just seven minutes was enough to give West Ham the win and prevent Tottenham from leapfrogging Leicester City at the top of the Premier League table.
After leaving behind cacophonous celebrations inside the stadium, Bilic said: "Spurs at home is always the game of the season for the fans.
"Spurs should be more happy with the result than us – it should have been more.
"To match the team that has conceded the least goals in the Premier League, has scored the most goals, is the best team in terms of running and pressing, and whose confidence is sky high, you have to play good football and have a really good game.
"But to outplay them and win against them without being lucky requires a great performance, and we were simply magnificent and I congratulate the players. The job they've done is amazing."
Bilic was quick to play down suggestions that his side could make a late push for a top-four finish and claim a spot in next season's Champions League.
The result leaves West Ham just one point behind Manchester City in fourth place, but Bilic said: "We are not thinking about the top four and we shouldn't be thinking about it.
"The gap might be small for those places but there is also a small gap between us and seventh, eighth, ninth or 10th place.
"We are going to approach the remainder of the season very confidently."