Scott Carson was at full stretch to tip a header from Brentford's John Egan behind, while Tom Ince saw his free-kick turned over by visiting keeper Daniel Bentley.
The visitors almost scored when Scott Hogan rounded Carson, but he could only find the side netting.
Derby, who have just seven goals in 13 games, are three points off relegation.
Johnny Russell and Ince had the Rams' best second-half chances, while Romaine Sawyers had a penalty shout waved away for Brentford.
Despite the lack of goals, Steve McClaren's Derby side are now on a four-game unbeaten run, conceding just once in the process.
Their lack of attacking impetus was compounded by James Wilson's knee injury in training, and they also lost Will Hughes, who limped off midway through the first half.
Brentford, winless in three games, are just a point outside the top six and rarely looked in trouble against their hosts.
The clean sheet was their first against Derby in 11 attempts, going back to 1953, and they have not won an away game against the Rams since 1939.
Derby County manager Steve McClaren:  "The first half was too slow, no tempo and a little too safe.
"But we've got to play football with these players, they are football players, we can't play long ball.
"At times they are making mistakes but that will progress and will get better and I had no faults apart from in the final third where we needed that bit of magic.
"A draw was probably a fair result, we huffed and puffed without blowing the house down."
Brentford head coach Dean Smith: "I don't know if we deserved to win but we certainly deserved a penalty.
"It was a double whammy and how it's not given I don't know. I think their bench was embarrassed it wasn't given as well.
"I thought our performance was very good, very disciplined and the intensity of pressing in our half was very good.
"Derby have got very good players but had very few clear-cut chances and I think our goalkeeper was rarely troubled.
Match ends, Derby County 0, Brentford 0.
Second Half ends, Derby County 0, Brentford 0.
Craig Bryson (Derby County) wins a free kick in the defensive half.
Foul by Ryan Woods (Brentford).
Attempt missed. Josh Clarke (Brentford) right footed shot from outside the box is high and wide to the right. Assisted by Romaine Sawyers.
Foul by Craig Bryson (Derby County).
Lewis MacLeod (Brentford) wins a free kick on the left wing.
Substitution, Brentford. Lewis MacLeod replaces Sullay Kaikai.
Attempt missed. Romaine Sawyers (Brentford) right footed shot from the left side of the box is just a bit too high. Assisted by Sullay Kaikai.
Substitution, Brentford. Josh McEachran replaces Nico Yennaris.
Substitution, Derby County. Darren Bent replaces Matej Vydra.
Cyrus Christie (Derby County) wins a free kick on the right wing.
Foul by Sullay Kaikai (Brentford).
Attempt missed. Craig Bryson (Derby County) right footed shot from outside the box is high and wide to the right. Assisted by Tom Ince with a headed pass.
Tom Ince (Derby County) wins a free kick in the attacking half.
Foul by Sullay Kaikai (Brentford).
Hand ball by Craig Bryson (Derby County).
Foul by Tom Ince (Derby County).
Yoann Barbet (Brentford) wins a free kick in the defensive half.
Substitution, Brentford. Josh Clarke replaces Sam Saunders.
Attempt saved. Johnny Russell (Derby County) right footed shot from outside the box is saved in the centre of the goal. Assisted by Ikechi Anya.
Attempt missed. Johnny Russell (Derby County) left footed shot from the centre of the box misses to the right.
Attempt missed. Scott Hogan (Brentford) right footed shot from a difficult angle on the left is close, but misses to the left. Assisted by Nico Yennaris.
Craig Bryson (Derby County) is shown the yellow card for a bad foul.
Foul by Craig Bryson (Derby County).
Scott Hogan (Brentford) wins a free kick in the attacking half.
Corner,  Derby County. Conceded by Andreas Bjelland.
Attempt blocked. Cyrus Christie (Derby County) left footed shot from outside the box is blocked. Assisted by Jacob Butterfield.
Substitution, Derby County. Johnny Russell replaces Chris Baird.
Attempt missed. Tom Ince (Derby County) left footed shot from outside the box is too high. Assisted by Matej Vydra.
Scott Hogan (Brentford) is shown the yellow card for a bad foul.
Scott Carson (Derby County) wins a free kick in the defensive half.
Dangerous play by Scott Hogan (Brentford).
Attempt saved. John Egan (Brentford) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Sullay Kaikai with a cross.
Corner,  Brentford. Conceded by Scott Carson.
Attempt saved. Romaine Sawyers (Brentford) right footed shot from the centre of the box is saved in the bottom right corner. Assisted by Sam Saunders.
Foul by Ikechi Anya (Derby County).
Sam Saunders (Brentford) wins a free kick in the defensive half.
Attempt missed. Sam Saunders (Brentford) right footed shot from outside the box is too high. Assisted by Romaine Sawyers.
Delay over. They are ready to continue.
Derby's struggle for goals continued as they were held to a frustrating stalemate by Brentford.