The Midlands club struggled to create chances in the first half, with Watford the dominant side. However, the team held on to their clean sheet and allowed Steven Davies to put them ahead soon after the break.
"The first half was not very good at all and we knew we had to improve," Clough said.
"I think the difference between this and when we came here last season - we were 3-0 down at half-time and played better than we did in the first half today - but we've got a bit more resistance about us at the moment.
"The goalkeeper, the two centre-halves are different from this time last season and I think it showed."
The Rams will next face Blackpool at Bloomfield Road on Wednesday.