McClaren was appointed as head coach at the start of October shortly after Clough's surprise sacking on September 28 following the Rams' 1-0 defeat to east Midlands rivals Nottingham Forest.
On Saturday, Derby thrashed Blackpool 5-1 at the newly-named iPro Stadium to record five straight Championship wins for the first time since the promotion-winning campaign of 2006/07.
Since McClaren took charge the Rams have won seven and drawn two of their 10 matches and the only defeat was a narrow one, away at QPR.
The former England boss said: "We are getting a good balance to the team but credit to Nigel Clough for bringing these players together.
"It was a big call from (chief executive) Sam Rush to do what he did and all we have done is just come in and try to justify that decision and justify that belief Sam had, not only in myself but Paul (Simpson, first-team coach) and Eric (Steele, goalkeeping coach), and what we could do.
"I give all the credit to the players. We said when we came in that this team can play good football, is a good team and a good squad. It was just inconsistent.
"We want to get consistency and we are getting that at the present moment.
"We have to keep our feet on the ground. Results bring expectation but we know we have still got a lot of work to do and a long way to go."
McClaren also feels he has learned more about his Derby players in the past week than he had in his previous nine weeks at the club.
Saturday's victory over Blackpool came on the back of a win at Wigan and another three points at home to Middlesbrough and cemented Derby in fourth place in the table.
Looking back on what he called a 'big week', McClaren, who succeeded Clough at the start of October, said: "There has been lots of challenges and tests for the team and the squad during that time.
"They have come through the challenges and won each of the games differently.
"They have fought when they have had to fight and have played good football when they could.
"It is all very pleasing. I think we have learned more in those six or seven days than we did in the rest of my time here."