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 3-2 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."