The Baggies slipped to defeat on Saturday to extend their winless run in the Premier League to nine games – a result which leaves them languishing in 15th place.
Rajiv van La Parra scored the decisive goal a minute short of the break with a stunning long-range effort, before Huddersfield were reduced to 10 men following Christopher Schindler's second yellow card early in the second half.
West Brom struggled to break down the hosts' resolute back line despite their numerical advantage and Pulis concedes that his players might struggle with the pressure to return to winning ways.
"I am disappointed professionally - it hurts to go such a long time without winning a game," he told BBC Sport . "But things conspire against you at times and you don't get the breaks. I worry about my players more than anything else, whereas I've been in this game too long to be affected by any criticism."
"You can't fault my players, who have worked incredibly hard. But we are in the results business and these results mean there's some pressure on me.
"When they went down to 10 men there were times when we could have displayed a little more care in the final third."
Pulis' counterpart David Wagner, meanwhile, was left to celebrate a second consecutive win at the John Smith's Stadium – two weeks after a famous victory over Manchester United.
The German has guided his side to three triumphs in six home games this season and believes this win was every bit as significant as the one over Jose Mourinho's side.
"This is one of the highlights since I arrived at this club. Two weeks ago we beat Manchester United but the win today was another big moment for this club," he said.
"The support here was amazing, just electric. The crowd played their part today as we got the result over the line.
"Look how my players worked, what they left out there on the grass. It was an absolutely deserved win today and I am delighted for my players because the workload was unbelievable. It was a great afternoon for us."