The Hammers have shown signs of improvement over the past fortnight thanks to four points from six against Huddersfield Town and West Bromwich Albion, having lost their opening three games of the campaign.
Bilic saw the pressure continually grow in the first few weeks of the season but, ahead of this weekend's showdown with Spurs at the London Stadium, Antonio is confident of putting three more points on the board.
"We always turn up against Spurs," he told talkSPORT. "It's a massive occasion and we always want to do it for the fans.
"The team are right behind the manager. It shows in the last three games, and hopefully we can keep building on it and moving forwards. With the bad start we had, the last three games have been positive. So hopefully we can build on that, score more goals, and I can get on the scoresheet myself."
West Ham, who find themselves 17th in the Premier League table, also made it through to round four of the EFL Cup in midweek with a 3-0 win over Bolton Wanderers.