West Ham have won just three times in their opening 11 games and have an ominous route to the Christmas period.
They face Tottenham, Manchester United, Arsenal and Liverpool in their next four league games – as well as United again in the EFL Cup – taking them into mid-December.
Rather than fearing the worst, Bilic insists meeting the big boys can inspire his players.
“It’s a very tough schedule,” said Bilic. “But we have seen how we played against top teams last year.”
Last season West Ham beat Liverpool home and away and picked up another 11 points off Tottenham, United and Arsenal on the way to an impressive seventh-placed finish.
West Ham’s big problem has been in front of goal.
They have scored just 11 times in the Premier League and new signings Andre Ayew, Simone Zaza, Ashley Fletcher and Jonathan Calleri have yet to open their accounts in a combined 869 minutes of action.
Diafra Sakho is back in training and will be available for the next match against Tottenham and Andy Carroll is beginning another road to recovery.
On Saturday their opener came thanks to a Dimitri Payet cross and Michail Antonio’s head – although Glenn Whelan was later awarded an own goal after his deflection changed the trajectory of the ball.
Stoke striker Bojan Krkic came off the bench to equalise just 10 minutes later as Adrian rushed out and clattered Jonathan Walters.
The goalkeeper was booked and a penalty would have been awarded had the former Barcelona man not finished expertly from five yards.
But, despite having Darren Randolph in reserve, Bilic is not considering a change between the sticks.
“He is my No 1 for sure,” said Bilic of Adrian. “I’ve got no concerns about his form. OK, the goal was a big mistake from him.
“It’s a mistake but we should not forget how many times he has been key man for us.”
The point takes Stoke’s run to six games unbeaten and goes further to banish any doubts over Mark Hughes’ position as manager.
It took Stoke until October 15 to achieve their first win of the season but they are now comfortably positioned in mid-table going into the international break.
Premier League stats: Most shots so far in 2016/17
Fri, November 4, 2016Express Sport runs through the top 20 players who have fired off the most shots in the Premier League so far this season
Express Sport takes a look at who has had the most shots in the Premier League so far this season
And Hughes insists he always had the support of owner Peter Coates.
“Every team will have a run of five, six, seven games at some point in the season,” he said.
“When it’s at the beginning, people have a bit of a panic and think that’s how the season’s going to pan out.
“We just needed to get back on track which we have done and knew we would do. We get great support from the Coates family and I like to think I deserved a bit of support because I haven’t done bad for the club so there was never internal pressure.”