Yaya Toure believes Manchester City's performance in the Bernabeu shows they are almost at the same level as Real Madrid.
Cristiano Ronaldo scored a 90th minute winner to condemn City to a 3-2 defeat in their opening Champions League game, but Toure, 29, saw signs that the Manchester club have improved.
The Ivory Coast international, who set up Edin Dzeko for the game's opening goal, attributed Real's eventual victory, which came courtesy of late goals from Karim Benzema and Ronaldo, to their character.
"Madrid have fantastic character and a fantastic winning mentality and we are not far away from being a big team like Madrid," he told City's official website. "It is good to learn. We came to a big stadium and a big club and we wanted to show we are here, to show all the big clubs that Man City are growing every year. It is important we keep on going and continue to learn. Next time we will be stronger."
Toure, a Champions League winner with Barcelona in 2009, felt that Real were spurred on by reports of disharmony in their camp.
"We played fantastically well and I think Madrid had to win because they had a lot of speculation," he said.
City also face Ajax and Borussia Dortmund in their group and are three points behind the German champions, after Robert Lewandowski scored a late winner against their Dutch counterparts in the Westfalenstadion.
And Toure is well aware of the challenge they face to get out of the group stage.
"The draw for us is not so easy and we have to work with that," he added.