Despite a typically energetic performance, the midfielder was unable to stop Town falling to a 2-0 defeat away at West Ham United.
The goals were also the first Huddersfield have conceded upon their return to English football's top flight.
Mooy had a couple of half-chances during the game but wasn't able to draw saves from West Ham's English international goalkeeper Joe Hart.
The defeat leaves Town sixth on the Premier League ladder.
They next face Leicester City at home on Sunday (AEST).