Ward, who is on international duty with Northern Ireland this week, was brought to Pride Park from Sheffield United by Clough.
"I think the news surprised us all...the board obviously thought it was time for a change but the players thought it was harsh at the time," BBC Sport quotes him as saying.
"Now we have Steve McClaren coming in and he comes with a massive profile. He's a former England manager, he did well in Holland, he spent time in Germany, so it is an exciting time for the club now."
McClaren's first match in charge of the Rams saw them end their dismal record at home by overcoming Leeds United 3-1.