It looked like Derby would hold on to the 43rd-minute lead given to them by debutant Johnny Russell from the penalty spot.
But substitute Best, who struck the post with an effort on the hour, rescued Rovers a point two minutes from the end of regulation time with a superbly-taken volley.
"On the balance of the game, I thought it was a fair result actually," said Clough.
"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 debut with a confidently-taken penalty.
You could say it provided Derby with a spot of relief as the Rams had missed their previous four spot-kicks.
Clough added: "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."
- Sports & Recreation