Bilic had been facing mounting pressure following three opening league defeats but Monday's win over Huddersfield earned him some relief and his side their first points of the season.
West Ham remain 18th in the table, however, ahead of Saturday's game at West Brom and, having granted his players the day off on Wednesday, Bilic warned them against complacency.
"We were off yesterday and we had a meeting before training today [to say] if we think that because we beat Huddersfield we have done it - no," Bilic said.
"The difference between great players and good players is doing it every day or every week.
"It's down to both them and us to keep them in that zone - not to fly too high or be big-headed - it's a massive part of every manager's job.
"But it's also down to them to be like that. We can't control what they do outside the training camp.
"They are mature people though and are in a privileged position which most normal people would swap to be in. They should respect themselves by respecting the job."