Two second-half goals for Notts County gave Pools just too much to come back from, though Jones's men put in a battling display at Meadow Lane this afternoon.
It was a lively first half here, with Pools more than holding their own against the hosts.
Joe Fryer made an early save through a crowd of bodies from a freekick into the box, while Shola Ameobi sent a headed effort over the bar.
Mark Yeates forced his way into the box from the left to shoot at goal but Fryer blocked it at the near post.
Rhys Oates, again lively for Pools in his forward position, squeezed his way in between two Notts men to close in on goal but just lost out on the final ball as it was pushed from his path.
Lewis Alessandra, looking to add to his recent impressive tally of goals, cut into the box from the right wing to fire a shot in but his effort was deflected out for a corner.
Pools were putting in a real fight this afternoon, chasing every loose ball and battling all over the pitch in what was a much-improved away display.
And the measure of Pools’ performance came in the reaction of the home fans who became increasingly vociferous with their frustrations.
Lewis Hawkins put in a great challenge inside the box the clear the danger area before Fryer punched clear from a corner kick under pressure from Ameobi.
And the same trio were involved in the main talking point of the first half; a corner into the box was ruled to have been handled by Hawkins, with the referee awarding a penalty.
Shola Ameobi stepped up to take the spot kick, sending it out to Fryer’s right. But the big keeper showed quick reactions, getting down to the post and stopping the striker’s effort.
And from then on in Pools were on top for the remainder of the half; boosted by the penalty save.
Rhys Oates again tried to force his way between Bola and Duffy to get through on goal but was again denied as Bola stuck out a foot to clear.
With hesitancy showing in the County defence, Amond looked to take advantage as he pushed through on goal, using the bounce to beat the defender before a race for possession with Collin – which the Notts keeper just won.
The teams went in all square at half time but it was the hosts who got going first after the break, taking the lead within minutes.
Shola Ameobi broke forward with Scott Harrison on his heels but the former Newcastle striker showed his experience as he pushed on to send a low drive which beat Fryer and hit the back of the net.
After such a strong end to the first half, the goal was a blow for Pools who needed to show a quick reaction.
Nathan Thomas got on the end of a strong attack, which was kick-started by Oates, but his shot found only the arms of Collin.
Nicky Featherstone, playing as part of a back three this afternoon, got back to intercept a cross in from the left to deny Ameobi another chance on goal.
Liam Donnelly finished off another Pools attack with a low drive at goal from outside the box but his shot was held by Collin at the second attempt.
With 70 minutes gone, Notts County doubled their lead and made things harder for Pools; Jorge Grant let rip with an unstoppable strike from the edge of the box to make it 2-0 to the hosts.
But as is the way with Pools in recent games, they keep battling away and, less than ten minutes later, they pulled one back.
It was Nathan Thomas who had the shot, firing in from inside the area – his shot was blocked off the line but hit defender Haydn Hollis and went into the back of the net to give Pools a lifeline.
Pools were really positive in their play for the remainder of the game but just ran out of time to find an equaliser.
Full Time: Notts County 2 Hartlepool United 1
Attendance: 8653 (427 Pools)
Booked: Hakwins (28), Harrison (81)
Notts County: Collin, Tootle, Duffy, Hollis, Ameobi, Yeates (Smith 86), Forte (T Campbell 72), Milsom, Bola, Grant (A Campbell 90), Hewitt.
Subs Not Used: Loach, Dickinson, Clackstone, Howes.
Pools: Fryer, Richardson, Harrison, Donnelly, Featherstone, Hawkins (Deverdics 59), Woods, Thomas, Alessandra, Oates, Amond.
Subs Not Used: Bartlett, Martin, Hawkes, Orrell, Rooney.