In the end the Rams, with eight players in their squad under the age of 21, had to settle for a 1-1 draw after battling from a goal down.
Richard Keogh's own-goal in added time at the end of the first half sent Bolton into the break ahead. But Jamie Ward headed his 10th goal of the season nine minutes from time to ensure Derby deservedly took a share of the points.
Clough said: "It was a good point in the end when you're 1-0 down, but overall I think we deserved three.
"We created enough chances and restricted Bolton to very few opportunities.
"It makes it a little worse to concede an own-goal. He just got a little unlucky with it by getting the slightest touch on it - and the timing just before half-time didn't help us either.
"But we showed great character to come back and get a point, I'm absolutely delighted with the lads.
"We had several chances in the second half and when they don't go in you start to think it's not going to be your night, but then up popped Jamie (Ward) with a great header at the far post.
"It was a good goal, very difficult to control it when the cross is coming skidding in off the greasy surface like that. It was a very good finish indeed and no more than we deserved.
"We are sitting here with three points from out last four matches but we could quite easily have nine or 10."