Clough - whose Derby side have now lost four games in a row - said: "I thought we created the two best chances of the game and thought we had an absolute blatant penalty in the 92nd minute.
"Anywhere else on the pitch, a late tackle on Kris Commons, and he [the referee] gives a foul.
"When you have seen a player taken off on a stretcher after he's had a shot, I don't think there's any argument that that can be a fair challenge."
Warnock responded: "All the talking is trying to cover the cracks. Look at their bench. They've got a better side there than we have been able to put out. Let's complain about that."
On the late penalty shout, Warnock added: "I think I'd have to say an Arsene Wenger on that one and say which one was it? I didn't see it like the ref. It couldn't have been a foul or else he would have given it.
"On my kids' life I've not seen it.
"We gave absolutely everything and I'm proud as punch of my boys and I hope they get the headlines they deserve."
Palace goalkeeper Julian Speroni - who went on to be the Eagles' man of the match - was lucky not to have been sent off early on when he was only booked for picking the ball up outside the area under pressure from loan signing James Vaughan.
Derby's first shout for a penalty came just before the break when Rob Hulse appeared to be hauled down by Hill.
Johannes Ertl had a goal ruled out for offside for the hosts just after the restart.
Darren Ambrose got the vital winner on 55 minutes. He latched onto Shaun Derry's looping header which caught the Derby defence sleeping and the winger slotted past the advancing Stephen Bywater.
Ertl then rattled the crossbar with a powerful header from Ambrose's free kick with Bywater well beaten.
Hulse forced a reaction save from Speroni with a fierce drive straight at the Palace stopper as the minutes began to run out for the Rams.
But deep into injury time, Commons was in on goal before Hill clattered into the side of him. Speroni got a firm hand to turn his drive behind for a corner as the midfielder writhed around in agony.
Clough added: "We are short on confidence, we are short on luck and we are short on everything that we need to win football matches."