The Rams pulled off a remarkable 1-0 win over a weakened United side in the first leg of their semi-final tie last month.
And although Derby trailed 3-0 by half-time in the return leg, they almost forced extra-time as they eventually went down 4-2 at Old Trafford.
The two clubs meet again in the fifth round of the FA Cup this weekend and Clough reckons the Rams have given United boss Sir Alex Ferguson some food for thought ahead of Sunday's Pride Park clash.
"We showed we could cause them problems over the two matches, and certainly we did down here," said Clough.
"Defensively in the first half at Old Trafford, we weren't very good, and that is why we lost the tie at Old Trafford.
"But apart from that, going forward we created chances, scoring three goals in the two games, which is a rarity against United these days.
"Certainly, I think the home leg will have a bearing, even though there are bigger competitions in their eyes, given the Champions League and Premier League.
More cautious"I think they will be a bit more cautious. If they had come here and won two or three nil, he (Ferguson) would probably think he could put the same side out and do it again.
"But there will be a little doubt there, and in the players' minds as well we hope."
Regardless of whether United's stars are wary of Derby, Clough certainly believes his own players should have nothing to fear.
And he prepared his former club Burton Albion in the same way when they held United to a goalless draw before being knocked out of the third round in 2006.
"Another manager phoned and said to me, 'have you spoken to the players about their fears?'" explained Clough.
"I said, 'no', and he replied, 'well, I think you should'.
"That prompted me to say, 'well, if we start talking to them about their fears then they will have some!'
No fear"We don't want the players to have any fears, so the last thing you want to do is talk to them about it.
"It's been the same this week. If you run through their side the lads would be petrified.
"We all know how good they are, so there's no need to emphasise or highlight it.
"All we have to do is relax and play. There's no point getting too nervous, too het up.
"We just have to say, 'hold on a minute', calm ourselves down and play our stuff as well. It's very important we do that.
"So we're preparing exactly the same for them as for anybody, the same as it will be for Blackpool on Wednesday - which I hasten to add is a more important game for us."