On Tuesday, Madrid moved a step closer to the last eight of the competition with a 3-2 win over Malaga at the Bernabeu, after having fallen behind 2-0 at one point during the match.
Sergio Sanchez and Martin Demichelis scored in the 10th and 29th minutes to set Malaga up for an unlikely victory before Sami Khedira (68), Gonzalo Higuain (70) and Karim Benzema's strike 12 minutes from time completed the turnaround for the hosts.
"Our performance in the first half was not good. We lacked concentration and made big mistakes in set pieces, but my team cleaned its own trash thanks to the support of the crowd," Mourinho told the club's website.
"It isn't easy to find such support when you're losing. We came back thanks to the bond between team and audience, and we'll have the advantage [for the second leg] in Malaga.
"You'll have to ask the players why they changed in the second half. Why not do in the first half what you did after half-time? That'll be my question. I'll try to have them answer it for me as well as answer it myself. What matters is the result. It's important to win your first game at home; that's the primary objective in a tie in order to have the lead in the return leg."
Madrid striker Higuain, who was one of the goalscorers on Tuesday night, echoed his manager's sentiment after the game as well. The Argentinean declared it would be "hard for teams to beat us when the Bernabeu cheers us on" like they did against Malaga.
"It was a complicated game against a difficult opponent. We didn't do well in the first half, but we proved we wanted to win the game despite conceding two goals," he said.
"We'll have a victory advantage in Malaga, which is a very important thing to have in a two leg knock-out stage."
"We're grateful for the crowd's support.
"They had a lot to do in this comeback and I hope they continue to support us this way."
The winners of this tie will take on Barcelona in the quarter-finals if Pep Guardiola's men are able to see off Osasuna over two legs.