The defeat at Stade Gerland came three days after Real lost 3-2 at home to newly promoted Celta Vigo in La Liga.
"Despite such a heavy defeat, we need to keep calm because the competition is starting and we can't let ourselves become demoralised," Luxemburgo said after Tuesday's defeat.
John Carew, Juninho Pernambucano and Sylvain Wiltord all scored for Lyon in an 11-minute spell during the first half. It would have been worse had Juninho not missed a penalty in the 41st minute as the England captain, David Beckham, experienced his third defeat in less than a week, starting with last Wednesday's 1-0 reverse to Northern Ireland.
"They were lucky because they scored with their first free-kick and that decides lots of things," Luxemburgo said.
"In the second half we had opportunities and possession but the goal we deserved wouldn't come. The statistics show that we had a lot of opportunities but we didn't take them."
Madrid spent about £60m on five new players in the summer in an attempt to end a two-year trophy drought. Four played against Lyon - the Brazil forwards Robinho and Julio Baptista, defender Sergio Ramos and the Uruguayan midfielder Pablo Garcia. Only another Uruguayan, Carlos Diogo, did not feature.
Luxemburgo said his team suffered from the absence of Zinedine Zidane and the suspended Ronaldo. "They are two players who make the difference in a match," he said. "When Ronaldo isn't on the field, the opposing defenders are calmer. It's the same with Zidane, but they weren't there and we had to replace them," the Brazilian added.
Luxemburgo, who was appointed last December as Real's fourth coach in 18 months, must hope for an improvement when they visit Espanyol on Sunday.
In the corresponding game exactly a year ago, a 1-0 defeat provoked the resignation of one of his predecessors, Jose Antonio Camacho. Coincidentally, a few days earlier, Madrid had also lost 3-0 in the Champions' League - that time against Bayer Leverkusen.
Raul, the Real captain, said his side have to learn from their mistakes."We knew that Lyon were a good side," he admitted, "the difference was they took their chances. Now we have a few days to study the areas we need to work on."
As in Saturday's defeat to Celta Vigo at the Bernabeu, it was set-pieces that were Real's undoing. Carew flicked on a Juninho free-kick for the opening goal after 21 minutes and the Brazilian doubled the advantage with another free-kick from 35 yards, soon after.
"In football set-pieces are very important and, as against Celta, we conceded goals from them. We need to work on putting this aspect of our game right," Raul added. "There is still a long way to go and we hope this suffering will be a positive for us later on."
Iker Casillas, who saved Juninho's penalty, also recognised the need to work on their defence but did not believe the result was a fair reflection of the game. "Anyone who didn't see the game would think it was a mad result," said Casillas. "But no one needs to say anything to us because we are also very upset about it. Our luck will change though, we just had a tremendous amount of bad luck."
Gérard Houllier, the Lyon coach and former manager of Liverpool, was full of praise for his players. "We played a really good match against a very good Real team, no matter what the Spanish media say," he said.
While establishing themselves as the team to beat in France, Lyon have never quite made it in Europe, going out at the quarter-final stage of the Champions' League in the last two seasons.
"We can go a long way," said their captain, the Brazilian defender Claudio Cacapa. "This is good for our confidence but we must not get carried away," he added. "We have played just one match."
Some of the Lyon fans feared that their team's chances this season might have been hampered by the sale of Michael Essien to Chelsea. Yet the French champions also spent £28m on players in the summer and look at least as strong as last year.
Carew, Brazilian striker Fred and former Chelsea midfielder Tiago have fitted in quickly and are blending well with the likes of the playmaker Juninho, who was superb against Real.
Lyon are likely to get through a group also featuring Olympiakos and Rosenborg but are looking further ahead. "We want to do better than last season," said Jean-Michel Aulas, the Lyon president. "The fact that this year's final will be played at the Stade de France may be a sign."
Beckham's week to forget
N Ireland 1 England 0
A Beckham-led England suffer the embarrassment of World Cup defeat in Belfast against the team ranked equal 116th.
Real Madrid 2 Celta Vigo 3
Beckham is powerless to stop newly promoted Celta Vigo beating Real in La Liga. Fabian Canobbio's 77th-minute winner shocking 80,000 Bernabeu fans.
Lyon 3 Real Madrid 0
Real's galacticos are humbled yet again - this time at the hands of Gérard Houllier's Lyon in the Champions' League.