Former Chelsea striker Diego Costa scored four goals and was sent off as Real were embarrassed in New Jersey.
Joao Felix, a big-money summer signing from Benfica, scored his first Atletico goal before Real made a belated comeback from 6-0 down.
‘I’m not concerned, but I’m hurt,’ Real manager Zidane said at his post-match press conference, reported on the club’s official website.
‘You don’t play to lose. But we can’t be looking backwards.
‘It was a bad game and now we have to focus on what went wrong, so we can try and make sure it doesn’t happen again in the next match.
‘We don’t need to dwell on it, this is a pre-season game. They were better in every respect and that’s all there is to it.’
The build-up to the game was dominated by reports of Gareth Bale being set to leave Real and join Chinese club Jiangsu Suning.
Bale started on the bench and came on for the final 30 minutes of a game in which Nacho, Karim Benzema and Javi Hernandez scored for Real.
‘We can’t be pleased with this defeat, that much is clear,’ said Zidane.
‘We just really lacked the intensity you need at this level. But I’m convinced I’ve got a team here that is going to compete at the top level. We’ll be motivated and hungry to keep going, I have no doubt about it.
‘I’m convinced we’re going to have a good season. This won’t change what we’re looking to achieve this season. The players are not letting me down, we’re just preparing for the new season and we have to remain calm. We have to be ready for when La Liga comes around.’