Chris Eagles then levelled proceedings with a 41st-minute strike that beat Grant from 25 yards, which ensured a point for his side.
"I'm delighted with the performance and the manner in which we went about the game," Clough said.
"It was a setback going one-nil down early on, I thought it gave Bolton a huge lift but the way we came back and the way in which we played was especially pleasing.
"We conceded our second goal when we were at our most comfortable in the game. Granty came in, put his hand up at half-time and said he should have done better with it.
"And that's what's probably cost us the three points instead of the single one."
Derby have earned 10 of their 11 points this season on their travels, prompting speculation over what is the missing ingredient at Pride Park.
"We've played well at home in some of the games, not got the breaks and not scored the goals. Away from home we've just got the goals, that's it," Clough added.
"We've scored 12 goals in four games, which is incredible, I think, in four away games.
"We've defended a bit better away from home, we've conceded two but the first one's a good goal and the second one's a goalkeeping error, so apart from that Granty's not had too much to do."
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- Alex Baptiste
- Chris Eagles