The home side, without 12-goal top scorer James Vaughan with an ankle injury, had no-one to finish off the host of chances they created.
But Reading took all three points thanks to on-loan Sharp's second goal in three starts.
Robins said: "I am frustrated because we have done everything except the bit that Billy Sharp does.
"That's what strikers get paid for and that's why they get the plaudits they do."
Robins claimed his side should have had two penalties and insisted Huddersfield should have won comfortably.
"Reading would not have been able to complain if we had run away with that game," he said.
"We should have had two clear penalties which on another day we would have got and we would have come out clear winners.
"I am proud and pleased, and the players have done everything I could have asked.
"It's just in the penalty box, amid the muck and bullets, where we need to keep a cool head."
Huddersfield dominated the first 20 minutes and came on strong in the second half but failed to take their chances.
Paul Dixon and Danny Ward went close for the Terriers early on before Sharp, on loan from Southampton, grabbed what proved to be the only goal in the 32nd minute.
Jordan Obita fed Pavel Pogrebnyak who crossed for Sharp to head down at the far post. Town keeper Alex Smithies got a touch but could not keep it out.
Ward and Oliver Norwood both missed the target for Huddersfield before Martin Paterson struck a post in the 74th minute.
Sub Duane Holmes drove out of midfield and sent a pass to Dixon who cut the ball back for Paterson.
Town centre-back Joel Lynch was sent off in the fourth minute of stoppage time for his second bookable offence.
Robins said: "It was avoidable but we have to take it on the chin."
Reading manager Nigel Adkins praised his players and said: "We knew this would be a challenging fixture and it's good to come away with the three points.
"Billy Sharp scored the only goal but we could have scored three or four. We were very offensive in our mindset, we saw the game out and won quite comfortably.
"We have a really talented group of players from our goalkeeper and two centre backs to Jobi McAnuff in midfield and Pavel Pogrebnyak and Billy Sharp up front.
"We kept a clean sheet and showed good resolve and we utilised the whole squad.
"Huddersfield are a good footballing side and we know what a good job Mark Robins is doing.
"There were two good teams on the pitch but our victory was well deserved and it's another three points on the road."
Adkins was impressed with young keeper Alex McCarthy and said there he could force himself into England's World Cup squad.
He said: "In my mind he is a top four goalkeeper and if he stays with us for another year and plays regular football anything can happen.
"He is a confident lad, his shot stopping, command of his box and catching is first class. He can go to the top."