It was a night of contrasting emotions for Vaughan, who made it 10 goals for the season before the end of September, had another strike incorrectly ruled out for offside and struck the crossbar from a late spot-kick.
Describing his in-form striker's mood after such an eventful evening, Robins said: "He's devastated; he beats himself up so he's really disappointed.
"He feels like he's let everybody down, it's the end of the world, but he'll be okay again tomorrow."
Paul Ince's visiting outfit could have returned to the Sky Bet Championship's summit had they won by two goals and they were halfway there thanks to Ricardo Fuller's cool opener after 27 minutes.
Yet no player in the top four divisions has now scored as often as Vaughan this term and while the offside flag prevented him moving into double figures in the first half, he soon had the Terriers level after the break.
Then with six minutes to go, a breakaway attack was ended by Blackpool's Angel Martinez tripping substitute Sean Scannell from behind in the area to earn a second yellow card, but Vaughan squandered the chance to make it 11 goals in as many games.
"He was very unlucky," added Robins.
"But we've got to take those chances if we're going to climb the table. It doesn't get us any closer to Blackpool and they're in the play-offs.
"Even though it's the early part of the season we've got to keep believing and keep picking points up."
The game turned in the Terriers' favour thanks to two of Robins' changes, Scannell, introduced at half-time, and 18-year-old league debutant Duane Holmes whose perfectly-weighted pass provided the assist for Vaughan's 62nd-minute leveller.
Robins said: "I thought we were really poor first half. The changes had the desired effect and I was really, really pleased with the second half, as pleased with the second half as I was disappointed with the first half."
Blackpool assistant boss Alex Rae had no complaints about the decision to award Huddersfield their late penalty and argued a share of the spoils was a fair reflection given their dominance in the first 45 minutes.
"I'm led to believe it was a stone-waller," he said of Martinez's foul on Scannell.
"So I don't think we've got any qualms about that and, under the rules, it's a goalscoring opportunity so the referee has no other choice but to send him off.
"It's very difficult to come here and dominate for the full game and you have to give them some credit. They changed their personnel and changed their shape a little bit and we really struggled to get to grips with it.
"We're thankful to actually get over the line. I thought when the penalty opportunity came about...we'd have been really disappointed to come away with nothing."