The nine-times European champions had to come from behind with Cristiano Ronaldo powering in a header to level Danny Wellbeck's surprise 20th-minute opener.
Despite dominating possession Real were unable to turn their opportunities into goals, however, running into an organised United defence and an inspired David de Gea between the posts.
"I like to play first at home," Mourinho, who is chasing a third European Cup with a third club, told a news conference.
"That means you know what you have to do away in the second leg. Because of the English culture you can't play with defenders in your own box at home. United can't play like they did here."
The Premier League leaders endured a wobbly opening period, and after taking the lead against the run of play, then survived waves of attacks from the hosts after Ronaldo soared into the air to level after 30 minutes.
"We had chances to score more, but we were playing against a side defending very deep," Mourinho said.
"It's not a criticism. They can play how they like."
Real have three weeks to wait until the Old Trafford return on March 5, which comes just days after a King's Cup semi-final second leg against arch rivals Barcelona and a league 'Clasico' at the Bernabeu on the Saturday.
With Real trailing leaders Barca by 16 points in La Liga their chances of retaining their title are slim which makes securing a potential 10th European crown and, to a lesser degree the Cup, of even greater importance than usual.
Asked if Wednesday's result left him under greater pressure, he casually dismissed the idea.
"I don't feel any pressure," the Portuguese said.
"In the cup and the Champions League everything is all square [at 1-1] but we are Real Madrid and we can score goals and win games away from home.
"Many other teams have scored at Old Trafford and they haven't faced a team like us there yet.
"United didn't play to win but they did their job well. They will be happy. But they know what we can do there.
"If you asked me percentages I don't change one single number, it's 50/50."
