Curtis Davies had given Blues a 1-0 lead against the Rams but goals from Jason Shackell and Steven Davies secured a 2-1 victory for the home side.
"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," the new Blues boss told the club's official website, www.bcfc.com
"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.
"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."