The world champions looked on course for an important win in Gelsenkirchen before an injury-time equaliser from John O'Shea salvaged the visitors a point.
The result has left Germany in third place in Group D, three points behind leaders Poland.
"We blame it on ourselves," Boateng told Bild. "If you lose the ball that close to full time and concede a goal, you're practically begging for it to happen.
"We must clear the ball. It's just so cheap to concede a goal. This is a young team but also the youngest have played in the Champions League. This shouldn't happen to us easily."
Germany resume their qualifying campaign on November 14 when they entertain Gibraltar.