The 105th Derby della Lanterna saw Ciro Ferrara's Samp emerge 3-1 victors, thanks to goals from Andrea Poli and Mauro Icardi, with Genoa defender Cesare Bovo contributing a hapless own goal in the first half.
Del Neri threw on Juan Manuel Vargas and Andrea Bertolacci in pursuit of the draw, and Ciro Immobile did reduce the deficit, but the Grifone suffered a sixth consecutive loss.
It was Del Neri's fifth straight defeat since he replaced Luigi De Canio in October, but the former Samp boss believes he is the right man to turn things around at the Marassi.
He told La Repubblica: "Criticism is to be expected if you go on a run of five straight defeats, and I'll accept it if it's constructive.
"The club knew from the very beginning that this would not be an easy job and that we have been missing a lot of injured players.
"We all knew that there was a lot of work to do.
"I don't think that they have changed their minds, and neither have I."
Poli scored his first goal for Doria with a clinical turn and shot in the 16th minute before Bovo bumbled the ball into his own net shortly before the break.
Del Neri's double substitution saw Genoa tighten up and cut their opponents' lead in half through Immobile in the 73rd minute, but Icardi made the points safe at the death.
"There was a good reaction after the break, thanks to the quality of Vargas and Bertolacci," Del Neri added. "But unfortunately, it wasn't enough.
"That's a shame because at 2-1 down I thought the draw was possible, we had time to recover but lacked a bit of courage.
"The league is tight and we can get out of danger without too much fuss.
"The important thing is continuity and getting some good results. I don't think the club has changed their minds about me."
Sampdoria boss Ferrara had perhaps been under more pressure to deliver than his counterpart, with the Blucerchiati stranded in the relegation zone as a result of seven consecutive defeats.
But victory over the Grifone boosted Samp up to 14th and bought Ferrara some valuable time, with the 45-year-old telling La Repubblica: "It was written.
"We lost seven games just so we could win this derby.
"We've been through two difficult months and so I've given the boys one day off to enjoy this success.
"From Tuesday we'll be thinking about the next match. Only through continuity will we rediscover the confidence we had in the first five games.
"I have to thank the fans for how they have treated me over the last few months."