New boss Steve McClaren was denied back-to-back home wins by a battling Brentford side who deservedly held Derby to a goalless draw at the iPro Stadium.
There were few chances on a damp night in the east midlands but Derby twice had goalkeeper Scott Carson to thank for smart saves while substitute Johnny Russell was denied by a goalline clearance.
Tom Ince also went close for Derby near the end but Brentford more than deserved to bounce back from Saturday's defeat at Newcastle with a point.
Derby went into the game on the back of a serious injury to 20-year-old on-loan striker James Wilson who has returned to Manchester United after damaging a knee in training on Monday.
The home side created the first opening in the 18th minute when Matej Vydra caught Ryan Woods in possession and played in Ikechi Anya whose angled shot went behind for a corner and when Brentford only half cleared the ball, Ince fired just over from 15 yards.
Brentford responded with a strong run and cross from Sam Saunders which Romaine Sawyers headed wide from 10 yards before Derby made a change in the 24th minute with Craig Bryson replacing Will Hughes who had been moving awkwardly for several minutes.
The visitors were passing the ball neatly and they went close in the 36th minute when John Egan got on the end of a free-kick and forced Carson to turn the ball behind.
Daniel Bentley had to do the same when Ince curled in a free-kick from out on the right but the game needed a goal and Brentford almost supplied it in the 59th minute.
Sullay Kaikai skipped past Cyrus Christie and his low cross was touched on to Sawyers 12 yards out and he forced Carson into a smart save at his near post.
Brentford went close again in the 68th minute when Scott Hogan fired into the side netting from a tight angle but Derby nearly scored a minute later when Russell's shot was cleared off the line by Andreas Bjelland after Christie had crossed from the right.
The game was opening up and Derby were inches away from scoring in the 82nd minute when Anya went past three blue shirts on the left and drove in a low cross which Ince just failed to connect with as he slid in.
Brentford surged upfield and Kaikai played in Sawyers whose first-time shot from 18 yards just cleared the bar.
Anya made another strong run but Brentford's defence stood firm and the visitors went close in stoppage time when Hogan could not quite get a shot away after a cross had been touched on.