Clough felt his side could have been awarded a penalty when Peter Whittingham appeared to handle in the area late on.
However, he was also able to take several positives, having seen his side respond well to the setback of conceding an 11th-minute opener.
"Overall I'm very pleased with the performance," said Clough.
"We've generally played very well at home this season. This performance was a continuation of that really.
"We huffed and puffed (in the) second half. I thought we had a lot of the ball, even with 11 against 11, but they are extremely difficult to break down, with 10 or 11 men."
Derby have lost only once at home this term and Clough believes they are now seen as a force to be reckoned with.
"It's good when Cardiff come here and pay us a little bit of respect in the way that they play," he added.
"I think sides are worrying a bit more about us than they used to."