The Red Devils were two goals behind inside the opening 14 minutes at Estadio Nuevo Mirandilla, with Carlos Garcia and Anthony Lozano on the scoresheet.
Anthony Martial and then Kobbie Mainoo netted for Man United to level the scores early in the second period, but Cadiz scored twice more through Ruben Sobrino and Tomas Alarcon to secure a 4-2 win.
Ten Hag has said that the start was unacceptable, but the Dutchman is keen to "draw a line" under the result, with the team back in action against Real Betis on Saturday.
"It is quite clear. We were not awake, still sleeping, [in] first 15 minutes," Ten Hag told MUTV. "They are a threat in transition. We have seen, the second goal can't happen. We [were] not awake in the defence but also in the midfield we got ran off. It's not possible [and] it's not acceptable.
"After that, we came into the game and got a penalty. I think it was a clear one and I think maybe the second half [we] deserved another penalty, but the first one was a clear one. We came in the game, but we couldn't make the equaliser before half-time."
Ten Hag made 10 changes at the interval, with a number of youngsters given opportunities to impress, and the head coach was pleased with their work ethic during the second half.
"They gave energy. They run; they fight. Maybe not always in the right organisation, [so] they make mistakes [because] they are not used to playing in this level. It was a good lesson," he added.
"You see that if you make small mistakes, they have big consequences and that's what happened.
"The first 15 minutes cannot happen. That is not our standard and that should not happen. We've spoken about [the performance and] we'll do it tomorrow, again, but then we have to strike it, draw a line and then move on. But it can't happen in the future."
Meanwhile, Zidane Iqbal, who won Man United's first-half penalty, said that his side were always up against it after conceding "two sloppy goals".
"[We conceded] two sloppy goals and with it being our first game back after a little break, we will look back at it,'' Iqbal told MUTV.
''I thought we grew into the game and it's been a great experience overall, adapting to the weather and just getting my fitness up in the first 45 minutes.
''I thought the lads did well and they competed, but we are still learning, so some little mistakes ended up in goals. We are still on our journeys and I think we did well. We all have more to come.''
Man United will head back to Manchester following Saturday's clash with Real Betis to prepare for their EFL Cup fourth-round contest against Burnley on December 21.