Former United star Ronaldo levelled on 30 minutes with his seventh Champions League goal of the season, making him the top-scorer in the competition, after Welbeck had headed home a corner 10 minutes earlier.
Alex Ferguson had promised goals before the match and they came early enough, but then his team put on a battling performance with David De Gea excellent in goal to take a draw into the second leg at Old Trafford on March 5.
"They did their job well, they did not let us create space or score goals, but we can definitely score at Old Trafford, many teams have done already this season and they will know that," said Mourinho.
"Because of the football culture in England I don't think they can play as defensively there. We had chances to score more tonight, but they had a lot of men in front of the ball especially in the second-half.
"It's easy to understand, if they score first we have to score, if we score we're in the lead," he commented on the second leg.
Ferguson was happy with his side's performance and the result, picking out De Gea, Welbeck and Phil Jones for special praise.
"We would have taken 1-1 before the game. In the first-half I was disappointed at how deep we played, but the away goal is important, it is not finished but it gives us a good chance to go through.
"We'll play differently at home, they counter-attack very well but we have goals in our team, it's still 50-50 but the team that scores first will have a good chance." he said.
Sami Khedira had the first effort for the Madrid in the second minute when he pulled his shot well wide.
Next it was Angel Di Maria who tried his luck from outside the area before De Gea tipped a goal bound shot from Fabio Coentrao onto the post.
United weathered the early storm and when Welbeck and Shinji Kagawa combined well to win a corner on 20 minutes it was Welbeck who eluded the marking of Ramos to head home the opening goal and his first in the competition this season.
Ronaldo hammered wide the rebound of his own blocked free-kick before grabbing the equaliser 10 minutes later when he leapt above Patrice Evra to head home a Di Maria cross from the left.
Moments later Welbeck was inches from his second after good work on the left by Robin Van Persie and Wayne Rooney shot wide from the resultant corner.
Alonso then took a quick free-kick from his own half that put Mesut Ozil through and De Gea had to be quick to block the shot.
While Madrid continued to enjoy a lot of the possession in the second period, United still looked dangerous on the counter-attack and managed to restrict the home side to long shots.
De Gea made the save of the game on 61 minutes stopping Coentrao from close range with his outstretched foot.
Then Van Persie had two chances within a minute to restore United's lead with 20 minutes remaining.
The first shot was pushed onto the bar by Diego Lopez after Rooney had played him into space before he miskicked an easier chance.
United's defensive play grew throughout the game, the experienced Rio Ferdinand organised well the centre of defence, while Michael Carrick aided by Phil Jones and a very deep Rooney tidied up a lot in the centre of the pitch.
When Madrid did get through in the final minutes it was again Madrid-born De Gea who was at hand to save from Khedira on 80 minutes.
There was still time for Ronaldo to float a free-kick just over the bar and Diego Lopez to tip wide a Van Persie shot in injury time at the other end.