Borussia Dortmund took the lead when Robert Lewandowski's first-half strike on Wednesday was cancelled out by Real's Cristiano Ronaldo before Germany defender Marcel Schmelzer hit the 64th-minute winner for the German champions.
Dortmund snatched top spot in the group from Real to lead with seven points leaving Madrid on six and Ajax on three following their 3-1 win over Manchester City, who are last with just a point.
But with three group games left, Mourinho insists the English champions can still roar back to win their next three games -- home to Ajax, then Real, followed by a trip to Dortmund -- and remain a threat.
"Everyone knows this is a good group, some of the others are a joke, but this is a hard one," said Mourinho with Real set to face Dortmund again at Madrid's Santiago Bernabeu stadium in a fortnight.
"A big team will go to the Europa League and after this result there is a gap between us and the other teams.
"Us and Borussia are in the better position to make the next stage, but City can still get 10 points, so we have to make sure we get 11."
Cristiano Ronaldo looks dejected after his side Real Madrid lost to Borussia Dortmund in a Champions League game. Photo: AFP
Despite having been European champions nine times, Real continued their appalling record on German soil and in their 24 matches in Germany they have now suffered 17 losses and their single victory was 12 years ago.
"We were just missing a goal, both sides had their chances to win, we could have also got a few goals and won," said Mourinho.
"It was a strange match, neither team was better, but it was an incredibly difficult game.
"They were very organised and defended very well."
Having beaten Ajax 1-0 at home and only been denied a win at Manchester City three weeks ago by a late penalty in the 1-1 draw, the German champions produced another battling European display.
"It feels overwhelming, it was a sensational evening, you can only imagine something like this in your wildest dreams," said Dortmund coach Jurgen Klopp.
"Real Madrid are still the favourites in the group, but that's not bad for us."
Dortmund produced a highly disciplined display as they bounced back from losing the Ruhr derby 2-1 at home to Schalke in the Bundesliga last Saturday to claim victory despite only around 40 percent possession.
"A childhood dream has come true for me, I scored the winning goal against Real Madrid," said Schmelzer.
"When I took the shot I just wanted it to be on target. There were so many players standing in my path, I was sure someone would block it.
"It was important for us to show a reaction after losing at the weekend.
"We must be realistic, but we can also be consist in Madrid."
Having been heavily criticised after finishing fourth in their group in last season's Champions League competition, Dortmund defender Mats Hummels said his team are keeping their feet on the ground.
"We didn't take the criticism we received last year too seriously, but also we won't allow this success to go to our heads either," he said.
"We still haven't won anything yet."