After Paul Coutts cancelled out Ross McCormack's opener, Jake Buxton headed the winner in the 87th minute to give the Rams their third successive victory.
"We showed immense character but we should have done a bit better in the first half," Clough said.
"We were comfortable but we should have done more to get a goal in that spell. It took Leeds' goal to get us going.
"It was a great save by our keeper Frank Fielding from Sam Byram at 1-1.
"Frank hasn't had much to do in the last couple of weeks since he has come back in but that save was vital and I thought if anyone was going to score in the last 15 minutes or so it was us.
"I don't feel we are safe yet, but we want to finish on a high and get as many wins as we can."