A stunning Gareth Bale volley and two goals from Cristiano Ronaldo on his 400th appearance for the club gave Madrid a first win at Signal Iduna Park in the Champions League.
Pierre-Emerick Aubameyang got a goal back for Dortmund before Ronaldo made it 3-1 late on, and although the hosts produced plenty of attacking endeavour, only a handful of fine saves from Roman Burki prevented a more one-sided scoreline.
The Bundesliga leaders were particularly suspect at full-back, with Jeremy Toljan and Lukasz Piszczek frequently caught out of position on the counter-attack before the former was replaced by Mahmoud Dahoud after an hour.
Bosz insists it is a team effort to defend properly against sides of Madrid's calibre and felt they were always a step behind their opponents.
"We defend with 11 players and we attack with 11 players. You cannot blame the defence," he told SID.
"Against a very good opponent, who made almost no mistakes, we always were a step late.
"We need to defend better. We couldn't pressure the ball in nearly every moment of the game. That's what makes it hard against such opposition, who have quality. We have to analyse this and improve."
There was a moment of controversy three minutes before Bale's opener, when Maximilian Philipp turned the ball goalwards only to see it deflected onto the raised hand of Sergio Ramos.
Bosz felt it was a clear penalty but does not believe his side were hard done by in terms of the result.
"The moment in the first half was a penalty for a handball, clearly. But we deserved to lose," he said.
Dortmund, who lost to Tottenham in their opening match, sit second-bottom of Group H, six points behind Madrid and Mauricio Pochettino's side.