Tim Lemperle scored the visitors' winner early in the second half on Saturday to get a new-look Leverkusen off to a disappointing start after a summer of change.
Former Manchester United manager ten Hag, who took over from the Real Madrid-bound Xabi Alonso, had three new signings in his starting line-up: goalkeeper Mark Flekken, young forward Ibrahim Maza, and defender Jarell Quansah.
Quansah headed Leverkusen into an early lead, but Fisnik Asllani levelled in the 25th minute and turned provider for Lemperle in the 52nd.
The off-season departures of key players such as Florian Wirtz, Granit Xhaka, Jeremie Frimpong and former captain Jonathan Tah were evident as the home team failed to mount a response.
"It's tough because there's a lot of new relationships forming and so it's hard to build that rhythm exactly in the first game," Quansah said.
"It's not the end of the world that we're not exactly where we want to be. It's the first game of the season and we've got to understand that it's going to come with time."
Ten Hag was just one of four coaches making their Bundesliga debuts with new teams.
Former Germany assistant Sandro Wagner got off to a dream start with his Augsburg team winning 3-1 in Freiburg, while Paul Simonis also had an opening win with Wolfsburg beating Heidenheim 3-1 away. Horst Steffen's Werder Bremen lost 4-1 at Eintracht Frankfurt.
In other action, Borussia Dortmund held on for a 3-3 draw at St Pauli after Filippo Mane's late send-off for the visitors.
Dortmund were leading 3-1 when Mane was shown a red card in the 85th minute for taking down Abdoulie Ceesay, who was through on goal.
Danel Sinani scored the resulting penalty, and four minutes later Eric Smith sent the home fans wild when he equalised from distance.
15°C