It was the second straight loss in the competition by a three-goal margin for Ronald Koeman's side, following a defeat to Bayern Munich by the same scoreline two weeks ago.
It adds further pressure to Koeman, whose has come under immense criticism and could potentially be sacked amid a equally lacklustre start to the LaLiga season.
"It's a tough result to take, and it's not what we saw on the pitch," Koeman said.
"While we conceded early, we were good until it became 2-0. We had a number of chances to score and didn't take them. That's how you change games.
"If they score the three chances they create and we don't, then that's the big difference between the sides."
Koeman insisted the players were behind him as they bid to turn their form around, but he said he did not know if the board felt the same.
"I'm not going to argue about the level of my team. There's no point in comparing this with Barcelona teams of years gone by. That's as clear as water," the Dutchman said.
"I can only give you my opinion of my work at the club -- I feel backed by my players and their attitude. The rest, the club, I'm not sure ... I can't say any more, because I don't know what the club thinks in that sense. It's not in my hands."
Barca captain Sergio Busquets also said that part of the blame is with the players on the pitch.
"At the end of the day, they easy thing is getting rid of the coach, but we are all responsible. The truth is we're in a critical situation," Busquets said.
"We're only two games into the group stage. We need to focus on improving.
"We need to win our next two games against Dynamo Kiev and see how the other two get on. There's a long way to go and we need to try and be positive."
Uruguay star Darwin Nunez had two goals for Benfica on the night to lead the Portuguese powerhouse to the win at an electric night in Lisbon. Nunez's first goal came just three minutes into the game when he raced past Barca's backline and cut in on the left for the near-post finish.
Benfica's Lucas Verissimo then made a last-ditch block to deny Luuk de Jong from close range as Barcelona looked to get back into the game, but they were second best throughout.
Jorge Jesus' side continued to mount pressure after the break, with Rafa Silva doubling Benfica's lead in the 69th minute when he pounced on Joao Mario's initial shot.
Benfica continued the onslaught when Nunez saw a shot clip the wordwork after beating Marc-Andre ter Stegen to a through ball.
Nunez converted a penalty in the 79th minute after Sergino Dest was booked for a handball inside the box.
Barcelona finished the night with 10 men after Eric Garcia shown his second yellow card on the night.
Barca are at the bottom of Group E with no points from two games, six behind leaders Bayern and four adrift of Benfica. Dynamo Kiev are third place in one point.