The Rams took the lead through a first half penalty from debutante Johnny Russell, but Rovers claimed a point with a brilliant close-range strike from Leon Best a minute from full time.
"Over the balance of the game, I thought it was a fair result actually," Clough declared.
"They started the game well, then we changed it slightly halfway through the first half and got on top. Maybe over the course of the 90 minutes they had enough chances, so a draw might be fair.
"It's always difficult the first one, it's a big occasion for everybody and I'm delighted we didn't lose."
Russell, a summer signing from Dundee United, marked his Derby debut with a coolly-taken spot kick and Clough is pleased he has a reliable option from 12 yards.
"I'm glad we scored a penalty, because we have missed the last five or six! It's good we have got someone who can tuck them in. It's a good boost for him, getting a goal on his debut.
"It's just disappointing the manner in which we conceded the goal, and the lateness of it."
Asked if a finish in the top six is a realistic target, the Derby boss responded:
"We're aiming for it. There are going to be a lot of games where we are going to be nervous, hopefully we can get our noses in front, and be able to see it through."