Starting the campaign with three away games, the Hammers were without a point heading into Monday's clash at London Stadium, where goals in the last 20 minutes from Pedro Obiang and Andre Ayew secured victory.
And while Bilic acknowledged that it was imperative to take all three points, he says the pressure is nothing new.
"I am happy for the lads, I am happy for the whole club," he told Sky Sports. "It was a very important game for us. We started with three away games but three defeats; it was a must-win game.
"I am pleased with the way we played. Even if we hadn't won the game, I could say nothing to the lads. They gave everything.
"I have felt the pressure for a whole year now - it didn't start today. For me, it's not logical to be under pressure after three games, but it's modern football."
Andy Carroll, returning from injury to start, gave his backing to the manager after a big win on the Croatian's 49th birthday.
"I'm over the moon [to win for Bilic]," he said. "It's been disappointing to read a few things that are going on.
"But all the lads are behind him and it's a great win - for his birthday, it's even better.
"It was very important. I think we've had tough run. We needed three points and a clean sheet - that's what we got."