Christensen had initially been named in Xavi's starting XI for the match at Wanda Metropolitano, but he felt discomfort in his Achilles during the warm-up and therefore dropped out of the side.
"The idea was to start [Ilkay] Gundogan as an advanced midfielder on the right, the top of the 'box' as we call it," Barcelona boss Xavi told reporters after the contest in the capital.
"However, as Christensen couldn't play, we opted for Fermin [Lopez]. Christensen has some discomfort in his Achilles.
"Christensen is not injured per se. He has some Achilles discomfort, the same thing I had when I played. It's painful, but it depends on the day. Today he told us that he couldn't play."
On Monday, a statement from the Denmark national side revealed that Christensen had withdrawn from the squad for their March friendlies with Switzerland and Faroe Islands.
The 27-year-old will therefore remain in Barcelona with a view to being available for his team's next game against Las Palmas after the international break.
Xavi's side recorded an impressive 3-0 win over Atletico, with Joao Felix, Robert Lewandowski and Fermin on the scoresheet, and the result moved Barcelona onto 64 points, leaving them second in the table, eight points behind the leaders Real Madrid.
"We were brilliant in many stages of the match. We knew how to attack, the match was similar to the one against Napoli," Xavi told reporters after the game at Wanda Metropolitano.
"They pressed our centre-backs and we had to find space in behind, especially in the second half with Koke. We understood it well.
"I think this was the perfect match that showed our approach, our playing philosophy. We're very happy, everything went perfect and according to plan.
"This is a spectacular win, three golden points. This is the Barca that we want to see. As a manager, I am very happy today.
"Ever since I announced my decision to leave, the team is playing better. We're pressing more, attacking more, defending more. Our style is showing. Call it Cruyffism or whatever, but it's showing. Due to bad luck we don't play like this in every match, but when we do, it's so enjoyable."
Barcelona are unbeaten in their 10 matches since Xavi announced at the end of January that he would be standing down as head coach this summer.