A 1-0 weekend defeat by Levante was almost matched with Serrano's shot which forced Iker Casillas into the best save of the match.
Following a quiet opening, Racing threatened with a free-kick floated into the box by Papa Diop after 20 minutes but Xabi Alonso got up well to head out for a corner.
As the half hour approached Lassana Diarra tried a shot from long distance but that was off target.
Marcelo floated a cross into the Racing box as Madrid started to exert some control but the ball was too high for Cristiano Ronaldo.
Marcelo then fired a low cross from the left across the Racing box but Jose Maria Callejon just failed to get a touch despite lunging at the ball.
Ronaldo skewed a volley wide from a difficult angle and then the same player's cross was headed straight at Antonio Tono by Callejon.
Serrano brought the game to life four minutes into the second half with a left-foot shot which Casillas dived low to his left to turn around the post.
Gonzalo Higuain had a shot after cutting in from the right but Tono tipped the effort over.
Ronaldo was stopped by Bernardo Espinosa's strong challenge but hit the free-kick into the wall, Alonso firing the rebound wide.
Ronaldo then threaded a pass into the area but Karim Benzema was bundled away from the ball.
Marcelo whipped in a cross but Ronaldo just failed to get his head to the ball as another Madrid attack broke down.
The ball broke to Higuain in another Madrid attack but he fired into the side netting as the visitors' last chance went begging.