Appointed on Wednesday, Derry saw his side beaten by lower league opposition, but it was not really a shock.
Pools have now won seven of their last eight, with the Magpies bottom of League One.
The home side took the lead after 16 minutes, Jack Baldwin meeting Simon Walton's free-kick to head home.
But Notts were level less than two minutes later. Scorer Dean Leacock did not know much about it as Matty Dolan's clearance crashed off the County captain and bounced into the back of the net.
Luke James put Pools ahead again three minutes before half-time, reacting quickest after goalkeeper Bart Bialkowski spilled Michael Duckworth's shot.
In a tame second-half, Pools made it 3-1 after 75 minutes. James was quick off the mark again to net his eighth goal of the season after Dolan's free-kick hit a post.
Ronan Murray crashed in a shot from close range with six minutes remaining to get the visitors back within a goal but Derry's team could not force another equaliser to get a replay.