Second-half sub Steven Davies showed encouraging goalscoring form, netting a penalty and a header despite having played the majority of the game against Belper Town just 24 hours earlier.
The Rams were also delighted to have 19-year-old Arsenal midfielder Mark Randall play a full 90 minutes after the Gunners gave the green light to him linking up with County for the tour, which could result in a possible long-term loan deal.
Clough told the club's official website: "It was a highly competitive game and even had a bit of an edge to it, without ever having a silly tackle or risking players getting hurt.
"I thought Mark Randall did well for us; he is obviously a very talented footballer who is comfortable on the ball.
"Arsenal have been very good in allowing him to come and spend the week with us; this gives him a chance to take a look at our set-up and us an opportunity to see where he would fit in to our plans."