"I am happy for the lads and for the club. We started with three away games and three defeats and this was a must-win game.
"We had a game plan and from the first moment we were on the front foot. We stopped them from creating anything. We got our reward, a little bit lucky for the first goal but overall we deserved it.
"It is my birthday today and this is a great, great present for me," added the delighted Croatian.
The win took West Ham off the bottom of the table and up to 18th place, still in the relegation zone, while Huddersfield stay sixth with seven points from their four games.
Huddersfield manager David Wagner had no complaints about the result.
"We deserved this result; we were second best in everywhere and weren't good enough with the ball," he said.
"We have to be braver and more comfortable on the ball; we made too many unforced areas.
"It was an unlucky goal that we conceded but we have to be honest, West Ham were stronger today."