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The Terriers have now lost at home in all three major cup competitions this term and this was another poor effort in front of their own fans.
Clarke almost lifted the gloom of a dismal display when he tried a lob from just inside his own half. He spotted Rhys Evans off his line and the ball bounced over the keeper's head but came back off the bar.
Unfortunately for the home fans, eight-goal top scorer Gary Taylor-Fletcher took a touch instead of hitting the rebound first time and Shaun Barker snuffed out the chance.
That came just four minutes after the break with the game still goalless and had that gone in the result could have been different.
As it was the only goal came from the penalty spot when Clarke was adjudged to have handled Keigan Parker's cross and winger Wes Hoolahan confidently fired past Matt Glennon.
Adrian Forbes caused problems in the Huddersfield defence and was felled in the box by Joe Skarz seconds before and that looked a more certain penalty than Clarke's handball.
The first half was a virtual non-event and the only player to emerge with credit was Dublin-born Hoolahan, on a season-long loan from Livingston, who prompted and probed around the edge of the Huddersfield box.
He was always looking for the decisive pass and he created the best and arguably only chance of note when his corner found Keith Southern whose header was tipped over the top by Glennon.
Clarke's long-range effort just after the re-start sparked a revival for the home side, though in truth they couldn't get any worse.
Parker and David Fox joined Hoolahan to trouble the home side some more, although Jon Worthington and Michael Collins both had shots on goal go just wide for Huddersfield.
After the Seasiders went ahead in the 70th minute, Huddersfield mustered more resistance and boss Peter Jackson reshuffled the side by replacing midfielder Michael Collins with striker Luke Beckett.
A Beckett lob ended up on the roof of the net and Danny Schofield carved a way through the Blackpool defence only for Evans to pull off a fine save.
The home fans thought their side had levelled in stoppage time but Schofield's thunderous drive smashed into the side-netting and there was no end in sight to the Galpharm Stadium misery.