Notts County lost 2-1 at Victoria Park in Derry's first game since his appointment on Wednesday.
This was the Magpies' seventh successive away defeat, while for Pools it was a seventh win in their last eight games.
"The feeling is horrible," admitted Derry. "I spoke to the guys and said we don't want to be feeling like this again. They have too often this season but they gave me everything, like I asked on the first day I came through the door.
"If they do that then I will have no complaints, losing won't be down to attitude. I was pleased with attitude and determination and spirit and togetherness - everything you need to build a football club.
"I was disappointed obviously with the goals we conceded, but I think those who watched the game could see a dedicated and spirited performance and I'd like to thank the players.
"They gave me everything, but there's a lot to learn. Don't give silly free-kicks away constantly, we caused our own problems.
"Fair play to Colin Cooper, he has got Hartlepool in a great position in the league and into the second round of the FA Cup - which I would have loved.
"But I have learned that silly free-kicks, at any level, do that and you will concede goals. We have to stop those silly errors."
Hartlepool 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.