The Terriers twice hit back from going behind, but in the end both Yorkshire sides avoided relegation thanks to Crystal Palace's 89th minute winner against Peterborough, who dropped into the bottom three.
That goal triggered bizarre scenes on the field with players shaking hands before the final whistle and appearing to play out the final few minutes without any kind of incident.
Robins said: "It was the hardest 90 minutes that I've ever had to endure without a doubt. It was always going to be difficult.
"By no means were we at our best. We were a million miles from our best, but we got what we needed at the end of it.
"The game doesn't really matter. It was the outcome that counted. When you've got a cup final, you've just got to get what you need.
"I'm sure throughout that game we were fluctuating between relegation and survival and we've just managed to get our 58th point, which is an absolutely unbelievable total to be talking about anywhere near relegation.
"All the team around us have got an enormous part to play in that and deserve credit for making it as difficult as it was.
"That's got to be the hardest 15 games I've ever taken charge of because of the timing of it. It's been the most demanding two months of my managerial career.
"I'm delighted to still be manager of a Championship club because it would have been a disaster if we went down.
"The job David Flitcroft has done as well is nothing short of miraculous because they were dead and buried in January."
Chairman Dean Hoyle joked: "It was never in doubt. Seriously, it's been a tough day for both clubs. Barnsley have been on a roll with their form and we've done it on the last day which is fantastic.
"It's pleasing for Yorkshire. Huddersfield and Barnsley staying up and Hull promoted. It's a great day."