The Rams, looking destined for the drop to League One this season after having 21 points deducted, had come closest in the first half when Colin Kazim-Richards skied a glorious chance over from close range.
They were then denied by a fantastic save from Jed Steer after the break as Town’s on-loan Aston Villa keeper tipped Max Bird’s effort on to the crossbar.
However, Luton began to came on strong with the introduction of Danny Hylton and Cameron Jerome, the experienced pair combining for the only goal on 67 minutes as Jerome nodded Kal Naismith’s long ball down for an unmarked Hylton to pick out the bottom corner from the edge of the box.
It meant the Rams fell to yet another away defeat this season and remained eight points adrift of safety, as Rooney said: “I’m frustrated, we changed our shape, we gave Luton the respect they deserved, they’re not a team blessed with great individuals, but they’re a good, honest, hard-working team.
“I felt the changes we made really kept them at arm’s length, they didn’t have the impact they normally have in games, especially here, but we conceded a bad goal from our point of view.
“If we take one of our chances I think we win the game in a comfortable way, but we’ve lost it on a sloppy goal and didn’t take our chances.
“We have to keep working and keep fighting.
“I can walk out of this stadium as a proud manager and so can the players as what they are doing is tough.
“We have had challenges all season and just need to keep fighting, I believe we can do it, but we have to start turning results like this into wins.
“Our squad has no right to be in with a chance of staying in this division.
“This club is going through an horrendous time and I feel for the fans.”