A calamitous defensive performance in the first half, which made a mockery of the Reds' imposing recent strong rearguard statistics, saw Struber's side trail 3-0 at the break with the game effectively over at that point.
On a day when Struber's side could have moved outside of the drop zone with victory, they fluffed their lines spectacularly en route to a heavy four-goal loss at the bet365 Stadium.
Tyrese Campbell struck twice for the Potters, with strike partner Sam Vokes also netting in the first half, with two of the hosts goals before the interval arriving from corners when Barnsley switched off.
Substitute Tom Ince added a late fourth.
Struber was critical of his side's inability to cope with Stoke's set-piece prowess, which he felt his side had no answer to.
Attention now switches to Tuesday's huge game at bottom club Luton Town - who lost 5-0 at home to Reading - with Struber grateful for the opportunity to be back in action so far and he and his side seek to redress the balance after a sobering afternoon in the Potteries.
Struber said: "We did not show the face of the last games and it was a very bad face and we need to make a very big reaction.
"This is our responsibility and we need a completely different mindset. We did not have the right attitude after ten minutes.
"My responsibility and for every single player is to be self-critical with themselves and this is important.
"We have played four games and three from the four were very good. But today, we were not ready and have to change it.
"Especially after ten minutes when they got the second goal, I think it was a question of mindset for many players. They completely lost our plan.
"In set-pieces, they had a big advantage and we were not clear or ready at this moment. I think it was the game pressure for us.
"In the end, it was the big influence on this game. We had nothing from everyone and a very disappointing moment.
"In many situations, we had problems and not the right energy to win balls and play efficiently going forward. In every situation, on the ball and off it, it was not at the right level.
"They had a very good plan in set-pieces and we were always too late with our reaction. We were sleeping at this moment. This was the big issue. Against this massive opponent, you are not allowed to make this mistake."