Dortmund fought back from 2-0 down to level the match against the two-time defending champions thanks to Pierre-Emerick Aubameyang's quick-fire brace in Madrid on Wednesday.
However, the struggling German visitors – who were already out of contention for the last 16 – succumbed to a Lucas Vazquez strike with nine minutes remaining.
While Madrid boss Zinedine Zidane made five changes to his starting XI having already been assured of second place in Group H, under-fire Bosz played down their chances in the European competition.
"After today's game, I don't know if it is possible to say that Real Madrid are the favourite to win the Champions League," Bosz said during his news conference.
"They were not very strong tonight.
"Although, it is true that they rested many players and they are one of the favourites."
"We wanted to continue in the Champions League," Bosz added. "Now we will put everything we have into the Europa League.
"When the injured players return we'll improve. We still have to improve our level of performance, today went very badly. We showed at times that we can play football very well."
Bosz did single out Aubameyang, who has long been linked with a move to Madrid, with the Dutchman hopeful of keeping the Dortmund star.
"He isn't a player for Madrid... I'm joking of course," he said. "He has shown many times what a great player he is.
"He has speed and scores a lot of goals; I hope he will stay with us for many years."