Play was heavily affected across the four days, with no play occurring at all on Wednesday due to the downpours.
The hosts had put on 278 all out in their first innings, with Scott Elstone (63) and David Wainwright (54 not out) both making half-centuries.
Derbyshire then enjoyed the better of a rain-shortened third day as the visitors closed on 66-4, Mark Footit taking 2-28.
However, the weather put paid to any hopes of a finish and the draw was confirmed Wednesday lunchtime.
Meanwhile, the club is in Natwest Twenty20 Blast action Thursday and Friday.
On Thursday, Falcons host defending champions Northants Steelbacks at the 3aaa County Ground.
Then on Friday night Derbyshire travel to Headingley, when they face Yorkshire.