Rotherham boss Neil Redfearn was scathing of his side’s performance as his search for a first win in charge goes on.
The Millers have taken one point from Redfearn’s first four games at the helm and anything other than a routine defeat was never on the cards at the iPro Stadium.
The former Leeds boss was concerned about what he saw.
“That was not acceptable,” Redfearn said. “I accept the odd mistake now and again but not the lack of work-rate and wanting to win and that was apparent today.
“Players have got to take responsibility. You put a game plan together and they go out there, it’s up to the players to take the bull by the horns, and once we let them get in their stride we never laid a glove on them and that is really disappointing.
“They were worthy 3-0 winners to be honest. We have got a lot of work to do, we have got to bring some players, that’s a fact.
“At this moment in time I have got to see more from the players that have got the shirt, there’s got to be a desire and will to win.
“We are where we are, we know Derby are a good side but it has got to be more of a match than that.”
The Rams made hay through goals from Andreas Weimann, Jacob Butterfield and Richard Keogh and extended their superb run to nine games unbeaten, with seven wins.
This one, which kept them in fifth place, was never in doubt against a Rotherham side who are battling to revive themselves under their Redfearn’s new regime.
They carried no goal threat and dropped to bottom of the table ahead of Bolton’s late kick-off with Preston.
The Rams needed only seven minutes to forge an early lead as Weimann prodded home from eight yards after good work down the left by Craig Forsyth.
That gave them the platform they needed to lay siege on the Millers’ goal in the opening 25 minutes and they could easily have been further ahead.
Butterfield brought a strong save out of former Rams goalkeeper Lee Camp with a thumping 25-yard effort while Johnny Russell fired over and Weimann dragged wide.
The home domination was relentless and Bradley Johnson and Weimann headed over from dangerous set-play deliveries.
There was little chance of Derby’s wastefulness proving costly as Rotherham, playing one up front, had no penetration, with Jonson Clarke-Harris’ drilled free-kick the only time the otherwise redundant Scott Carson was tested in the home net.
And eventually their persistence paid off moments before the break as Butterfield powerfully drilled into the bottom corner from outside the area.
Rotherham improved after the break and enjoyed plenty of possession but were able to do little with it and it was the Rams who again threatened.
Weimann, who should have had a hat-trick, wasted another chance as he raced clear midway through the second half and saw his shot hooked off the line by Joe Mattock after lobbing Camp.
The third goal did arrive with 15 minutes remaining as Keogh rammed home from close range following a corner which had come after Chris Martin’s 20-yard free-kick had crashed into the crossbar.
The Rams threw on striker Darren Bent in the final 10 minutes in the search of an even heftier scoreline, but their work was done and as Paul Clement’s side look like building a promotion challenge, they are unlikely to enjoy an easier afternoon this season.