The 25-year-old, who scored 121 goals in six-and-a-half season at the Bernabeu, had been strongly linked with moves to both Juventus and Arsenal.
Albiol has been a part of world and European champion Spain's national team since 2007. He joined Madrid in 2009 from Valencia.
Handily for Mourinho it was Albiol who got Madrid off to the perfect start as he got on the end of Luka Modric's corner to turn in his first league goal in four years with the club.
Interestingly the decision comes when Marcelo has been suffering a low point in his career. He joined the club as an 18-year-old midway through the 2006-2007 season for six million euros.
As a result of Ramos red card, Morata was withdrawn after just 27 minutes as Mourinho looked to offer more defensive cover with the introduction of Raul Albiol but Karanka believes he did all that he could to show he is deserving of more opportunities in the first team.
Ronaldo became the latest Real player to be targeted by Mourinho when the coach reproached him following the side's unimpressive 2-0 Spanish Cup quarter-final first leg win over Valencia on Tuesday.
Spanish defender Raul Albiol said on Saturday the defending champions would be looking to beat Croatia in their final Euro 2012 Group C game on Monday.
Spanish defender Raul Albiol suffered a facial injury Sunday during training ahead of the final Euro 2012 Group I qualifier between the defending champions and second-placed Scotland.