"We started very poorly," the 54-year-old told his postgame news conference, adding: "But eventually you could see a team that can play good football and work together. We also showed that we have a lot of great players and it will be good for Dortmund's future when more return from injury after the winter break."

The Black and Yellows were too passive in the opening 15 minutes of the game, allowing Borja Mayoral and Cristiano Ronaldo to bring the hosts up by two goals within the first 12 minutes. Only after Real took the foot off the gas, the German side found their way back into the match. Eventually, Pierre-Emerick Aubameyang pulled one back for the guests in the 42nd minute before equalising four minutes into the second half.

Dortmund, however, could not hold onto what would have been their third point in Group H, as Lucas Vazquez's neat strike beat Roman Burki nine minutes before the end of regular time.

"We wanted to play more compact and you could see that we were not pushing as high up the field as we usually do," Bosz explained. "But if you play a bit deeper, you have to be all the more aggressive in those zones. We failed to be that and thus Real Madrid had it very easy to score twice on us. Afterwards, we had a lot of scoring opportunities but only converted one in the first half. In the second half, we started well [with the equaliser]."

Dortmund claimed the unwanted record of becoming the first team in Champions League history to secure a third-place finish on only two points after losing four and drawing two games. The Ruhr Side only remained ahead of Cypriot minnows APOEL on goal difference.

Bosz said: "Obviously, we wanted to remain in the Champions League after the turn of the year, but I have to say that we are deservedly not in this competition anymore. Now we have to do everything to reach as far as possible in the Europa League."

Asked by German broadcaster ZDF to sum up Dortmund's Champions League campaign in one word, Bosz replied: "Disappointing."

However, the Dortmund coach also took heart from his team's performance at the Spanish capital.

"We showed again, that we can also compete against such a team at the Bernabeu and played some great football in some phases of the game. We want to find back to winning ways."

BVB will be looking for their first Bundesliga win since September against Werder Bremen on Saturday with the help of Aubameyang, who bounced back from suspension with a brace and finding some extra praise of his coach.

He added: "Pierre-Emerick Aubameyang once again showed what great player he is. Not only by bagging a brace. His pace is a constant threat to his opponents. I hope that he stays with Dortmund for a long time."