Graeme Souness lost his job as a result of the Bristol City defeat, and this latest setback casts a dark cloud over Benitez's future at the club.
Benitez said: "I do not think the pressure on me is any different. When you lose there is always pressure.
"Frankly I am stunned and bitterly frustrated. The team are very upset.
"But we made so many chances and their keeper was the man of the match. I lost count of the times the ball was kicked off their line.
"We were ahead at the break and should have got a killer second goal. It is difficult to explain how we do not score from so many opportunities.
"You cannot blame any one player, but now we have to look to the next game against Inter. We cannot change anything now about Barnsley, we have to concentrate on putting things right in the next match.
"You cannot allow yourself to become down, we have to concentrate and pull together as a team."