Adler found himself facing an in-form attack from the visitors, who only secured their survival in the German top flight last season through the play-offs.
But Hoffe were did not show any sign of dwelling those struggles at the Imtech Arena, and went up after just five minutes through 21-year-old midfielder Roberto Firmino.
And despite pulling the match back level just before the half-way mark through Rafael van der Vaart's penalty, the break did not do the home side any favours.
The second spell saw Hoffenheim sink four past their opponents, including a brace from Anthony Modeste, and Adler was fuming with the team's performance.
"Our fans, I'm sorry if they have to pay money for this s***," he told Bild.
"It was an absolute disaster. 5-1, I say simply.
"It was a disastrous performance from anyone who was involved.
"I understand the displeasure of the fans. We need to score in the next game at (Hertha) Berlin."
Hamburg boss Thorsten Fink echoed his goalkeeper's concerns and
He added: "We got out in the first few minutes just fine and made it 1-1 at a psychologically opportune time.
"But it annoys me that we have fallen apart again. Our defence was very, very, very bad. That was a textbook case of how not to do it.
"We need to gloss over anything, but still look forward, and get back the credit of the fans. The objectives of the season are not reduced."
