Sir Alex Ferguson was too distraught to discuss Manchester United's Champions League exit after a night of high controversy at Old Trafford prompted José Mourinho, the victorious Real Madrid coach, to concede "the better team lost".

United led the Spanish champions 1-0, 2-1 on aggregate, when the Turkish referee Cuneyt Cakir showed a straight red card to Nani for a challenge on the Real defender Alvaro Arbeloa. Nani's challenge was high, but intent was debatable. A Wayne Rooney-less United had to hold out for over 34 minutes with 10 men but two goals in three minutes, from the substitute Luka Modric and the former United favourite Cristiano Ronaldo, denied the Premier League leaders a place in the quarter-finals.

Ferguson was so incensed at Cakir's delayed decision that he pushed his kit-man out of the way to race from the dug-out to the pitch. No stranger to avoiding press conferences, but not to avoiding controversial decisions on Champions League nights, such as the defeat to Bayern Munich in 2010, the United manager sent his assistant, Mike Phelan, to face all questions after the game.

Phelan explained: "I don't think the manager is in any fit state to talk to the referee about the decision. It speaks volumes that I am sat here and not the manager of this fantastic football club. We all witnessed a decision that seemed very harsh, possibly incredible at that moment in the game."

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The United manager had made the bold decision to omit Rooney from his starting lineup, raising fresh questions over the England international's long-term future at Old Trafford, but the tactic worked well with Real comfortably contained until the sending off. "If somebody can cry [over a harsh red card] then I am the first one," said Mourinho, referring to Pepe's dismissal against Barcelona in the 2011 Champions League semi-final. "My history is not to play against 10, it is to play with 10, and not in the last 16 or quarter-finals but in semi-finals. I want to be honest and to be honest is to say that in my opinion the best team lost. But that's football.

"When we were against 10 men we played very well for 10 minutes. We created new problems, with Luka and Kaká behind [Gonzalo] Higuaín. That was a new problem for United that they could not solve with 10 men. We deserve credit for that. After the two goals I knew what is Old Trafford, what is Sir Alex Ferguson as a leader and what he can do from a mental point of view. We could not control the ball by possession, which frustrated me. I thought we should but we could not.

"In that moment we had Diego López [the Real goalkeeper] who gave us the victory and that's part of the game. In Madrid, David de Gea was man of the match and today the man of the match was Diego López."

Before the game Ferguson explained the decision to drop Rooney was taken to allow Danny Welbeck to exert pressure on Real's "controller", Xabi Alonso, a policy that succeeded. Phelan added: "The decision was tactical. Everybody was fit, everybody wanted to play but big decisions have to be made and the manager made those calls. We had the balance just right.

"We got the tactics right. At 0-0 we were comfortable and where we wanted to be. Then we scored to put ourselves in a commanding position and were in control. Then the game totally changed. It is difficult enough to play a team like Real with 11 men. Now we have a distraught dressing room and a distraught manager. That is why I am sat here. It was a massive occasion, Ryan Giggs' 1,000th game and a worldwide audience. Like us, they are all probably wondering what has happened. A great occasion has been marred by one decision."

Ronaldo refused to celebrate his winning goal, one that keeps Mourinho on course to become the first manager to win three European Cups with three different clubs. "It was an emotional moment," said Ronaldo. "I can say only one word: unbelievable. The supporters made me feel shy, so I think in the two games I didn't play like I play all the time, at the same level. I feel happy because Madrid are through but a bit sad because United are out."

Mourinho added: "Mentally it was not easy for Ronaldo. I played at Stamford Bridge after I left. Not easy. I played Porto. Not easy. One day I will go back to the San Siro. Not easy. One day I will go back to the Bernabeu. Not easy. So Cristiano, not easy. It is not easy."

As for Ferguson's decision to omit Rooney from the side, the Real coach said: "I think Sir Alex has won the right to have every decision acknowledged as correct and every decision should have no question mark. He is the best, he has created history. You are nobody and I am nobody to put a question mark in front of him. His team was very well organised."