The winger does not agree with the notion that Manchester City were unfortunate to lose the game.
The Hammers ran out 2-1 winners at the Etihad Stadium on Saturday evening, bringing a halt to City’s five straight wins in the league, as well as being the first team to score against them in the Premier League this season.
It was an impressive performance from Bilic’s side as they registered their third away win of this season, having defeated both Arsenal and Liverpool on the road already during this campaign’s early stages.
Antonio has said that their new boss deserves all the praise for the win, revealing what he had told his side to do to secure three points.
"No-one's done it for ten years, so it has to be put down to him", the winger told whufc.com.
"He's told us our shape, he told us what we need to do to stay compact, what we need to do to counteract what they do, because they're quality players and they move the ball sharply, but we've managed to come out and do it."
'It's about how we set up and performed'
Despite having lost the game, City received praise for the performance that they put in, with many suggesting that they were unlucky to lose on the day.
That train of thought, though, completely neglects to mention just how well West Ham performed to secure the victory, their first away at City in 10 years.
Antonio has rejected the idea that the hosts were unlucky at the Etihad, saying the result is more about how well his side performed rather than City’s failure to win.
“It's now how City didn't win the game, it's about how we set up and how we performed,” he added.
“We didn't make it easy for them, we were hard to break down. They had opportunities because we stayed deep to defend the lead.”