Goals from Richard Keogh and Chris Martin proved enough to earn County their first win in nine games, although they were on the back foot for much of the second half after Jeff Schlupp halved the deficit.
The win hauled Derby six points clear of the relegation zone, although Clough admitted their performance was far from their best.
"It was probably the worst we've played at home this season in terms of the football we played," he said.
"But in terms of determination and sheer bloody-mindedness, that was as good a three points as we've had in the last few seasons.
"Our defending was a little bit better. We conceded one which we're not too happy with but I thought generally we had people throwing themselves at the ball on the edge of the box and the two centre halves were outstanding.
"The results before the game put us in a more precarious position than we would have liked so it's a relief for everybody. We should not be in this position - but we are."
Martin is due to return to Norwich as his loan deal expired after the game, but Clough hinted he may be able to keep him at Pride Park for the remainder of the season.
Clough added: "I think Chris wants to stay and that's the main thing."