A desperate display in the opening 45 minutes saw the Hatters race into a 3-0 lead on an afternoon when youthful Barnsley's lack of Championship experience looked painfully obvious.
The hosts - who made two tactical changes at the interval with Mads Andersen and Daniel Pinillos replaced - did show some fight in the second half, with Mallik Wilks netting a consolation with his first goal for the club on 72 minutes, but the damage had already been done.
Stendel, whose side's run without a win in all competitions extended to four matches with Luton racing into a 2-0 lead inside five minutes, said: "We need to apologise for the first half. The supporters can expect more from us, especially in a home game.
"I think it was the worst case in (terms of) what could happen today. It was a big chance for us to take our second three points, but our start was so bad.
"You can say we were insecure. The performance in the first half was a result of our start. We tried to change things and the feeling for the players on the pitch.
"We had prepared for the game and the atmosphere and feeling was good. But we cannot play like this in the Championship and it was a big experience in the game today.
"We need to come back to our best performances and every player has the time before next week to show me that he can play against Wigan.
"The more things you can learn in the worst situation and for me it was the case today. Next week is another game.
"We don't have any players with 200 games in the Championship. This is the situation at the minute."
A tough day was compounded by the sight of Bambo Diaby hobbling off with a leg injury midway through the second half and the big defender will undergo a scan.
Meanwhile, Stendel said that it is unlikely that Cauley Woodrow will return for next weekend's game with Wigan.
On Diaby, he said: "It looked not good. I have no (further) information. We will see. The first feeling is that it is a bad injury."