Aleksandar Mitrovic’s penalty four minutes from time had looked like rescuing a point for the Magpies to keep them three points behind their hosts.
But Martin Olsson scored in stoppage time to earn Norwich a vital win which leaves Newcastle 19th and six points adrift of safety with seven games to go.
“It’s really painful,” Benitez said. “We cannot change things. The only thing we can take as a positive is the reaction of the team, but we have to do it also in the first half.
“We didn’t play well in the first half. We didn’t play as I was expecting.”
Asked if he still believes survival is possible, the Spaniard said: “If we can fight and play like we played in the second half, yes. We have to try to keep this level for 90 minutes in the next game and for the next seven games.
“We have seven games to play and we have to start winning as soon as possible.”
Alex Neil’s men had appeared to have thrown victory away, but now the Canaries can further boost their survival bid against Crystal Palace and Sunderland in the next two weeks.
Mitrovic came off the bench to cancel out Timm Klose’s first Norwich goal.
Dieumerci Mbokani scored three minutes later to restore the hosts’ lead, but Mitrovic then converted from the spot after Gary O’Neil was penalised for handball before Olsson’s winner.
Swiss defender Klose, a January signing from Wolfsburg, now hopes the Canaries’ luck has turned.
They can draw level with 16th-placed Crystal Palace by winning at Selhurst Park next Saturday and play Sunderland at home the following week in two games key for their survival.
“Some games before we’ve not had luck on our side,” Klose told Norwich City TV.
“This time we did, and it felt fantastic to win the game. I’m very happy at the moment because we’ve got two big wins in our last two games.
“We’ve got more big games coming up. We want to take points from those as well.”
Olsson’s strike was his first since September 2014.
“It’s a really good win for us,” the Sweden left-back said. “We were thinking about this game ahead of the international break.
“It was good to get out on the pitch and get the three points. The only thing we had in our mind was winning. We didn’t want to draw so we went for it at the end and got the luck. I hardly ever score, so it was a great feeling.
“I didn’t know how to celebrate so I just ran around like a headless chicken. We have to keep playing well in order to keep this going.”
Ruddy, Wisdom, Bennett, Klose, Olsson, Jarvis (Redmond 75), Howson, O’Neil, Brady, Naismith (Hoolahan 81), Mbokani (Jerome 85).
Bassong, Bamford, Rudd, Mulumbu.
Darlow, Janmaat, Mbemba, Taylor, Anita (Mitrovic 62), Shelvey, Tiote (Perez 46), Townsend, Wijnaldum, Sissoko, Cisse.
De Jong, Lascelles, Riviere, Woodman, Sterry.