It was only Huddersfield's first defeat on their return to the top division after a 45-year hiatus, but Wagner is keen on setting a high benchmark early in the campaign.
The hosts were rewarded for their dominance in the 71st minute when Pedro Obiang opened the scoring with a deflected effort from distance.
The defeat leaves Town sixth on the Premier League ladder.
Instead, West Ham achieved a scratchy 2-0 victory that temporarily eases the pressure on Bilic and Huddersfield were the team handed a reality check.
"We had a gameplan and from the first moment we were on the front foot and we were really closing them down. If we have learned that lesson then I accept this".
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"He deserved this because he has been under a lot of pressure of course as we all know. It is my birthday today and this is a great, great present for me".
Andy Carroll has been mocked for his armed robbery ordeal by former West Ham midfielder Martin Allen.
And the Croat, celebrating his 49th birthday, has also had public disagreements with the club's owners over their failure to sign his key target William Carvalho, as well as Renato Sanches and Grzegorz Krychowiak. We were good in seconds and defended their set pieces ok. "We made so many unforced errors".
The 27-year-old Senegal global is available for Monday's Premier league visit of Huddersfield Town as Bilic hopes to avoid a fourth straight defeat.
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