First-half goals from Jason Shackell and Steven Davies secured victory for the Rams after Curtis Davies had put Birmingham in front with a header from a corner.
Hughton told his club's official website: "I certainly felt we were unlucky not to pick up a result, but the great thing is that there are plenty of positives to build on going into the Coventry home game next weekend.
"We deservedly went ahead and at that point were in control. However, we conceded two goals where we could have done much better and that changed the game.
"Things really opened up at that point and there was space on the pitch. We pushed on again and no-one can fault our desire in trying to get an equaliser.
"We took the game to Derby and I think the 4,000 supporters - who were magnificent today as always - appreciated that."
Hughton handed debuts to five players and was satisfied with the overall performance of his new-look side.
"They have had very little time to gel but that being said no-one would have thought so with how we played for large parts of the game," he continued.
"We hit the woodwork on a couple of occasions and had those chances gone in it may have been a bit of a different story, but we also need to work on having a bit more guile when we are attacking.
"It was a step in the right direction and there were plenty of positives to build on."