Madrid were beaten by the German champions, dropping their first points of the group stages, but remain on course to qualify for the last 16.
They return to action in the La Liga on Sunday with a trip to Real Mallorca, where they will hope to make it four wins from five league games following their dreadful start to the season.
The reigning champions managed only four points from the opening four games but since then only Barcelona have taken points off Mourinho's side, with a 2-2 draw at the Nou Camp earlier this month.
Madrid coach Jose Mourinho said: "We are not used to having so many defeats at the start of season but we need to take a look at the matches. Dortmund played more tightly than we did.
"We have matches in league and cup coming up and we need to go and win those."
Mourinho was given more injury concerns last night after Sami Khedira hobbled off with a thigh problem to join Marcelo, Fabio Coentrao and Alvaro Arbeloa on the sidelines.
Mallorca sit three points and four places below Madrid in eighth place and will aim to bounce back after last weekend's narrow defeat by Sevilla.
Although Barca are well clear of Real Madrid, they still have a team from the capital hot on their heels, with Atletico Madrid also having dropped only two points.
The key to their performances has undoubtedly been the form of star striker Radamel Falcao, who has scored nine goals already, and he will aim to net in a seventh successive league game against bottom side Osasuna on Sunday.
Fifth-placed Sevilla travel to Real Zaragoza and Levante meet Granada while Athletic Bilbao host Getafe. On Monday, Real Sociedad travel to take on Real Valladolid.
Barcelona moved clear at the top of the La Liga table for 24 hours at least with a thumping 5-0 win at Rayo Vallecano
Real Betis moved up to fourth with a 1-0 home win over Valencia.
Salva Sevilla scored his first goal of the season on nine minutes after Juan Carlos' cross was not properly cleared by Adil Rami.
Adrian ensured the win, and his third consecutive clean sheet since taking over as the first-choice goalkeeper, when he kept out Roberto Soldado's late effort with his legs.
Celta Vigo claimed a 1-1 draw in their Galician derby with Deportivo La Coruna despite playing with 10 men for 40 minutes.
Mario Bermejo gave Celta an eighth-minute lead only for Juan Dominguez to equalise 21 minutes later.
Celta then had Gustavo Cabral dismissed for a second caution on 52 minutes but the visitors failed to make the extra man count.
Third-placed Malaga failed to close on the leaders as they were held to a goalless draw against struggling Espanyol at the Cornella El-Prat..
Atletico Madrid vs Osasuna
Real Valladolid vs Real Sociedad