Manuel Pellegrini's men exited the competition on Wednesday after a 1-0 loss at the Bernabeu without registering a single shot on target, a week after holding the Spaniards to a 0-0 draw at the Etihad Stadium in the first leg.
Their impotence led Keane to question whether City even believed in defeating los Blancos, claiming they were simply content to play in their first-ever European semi-final.
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The Champions League winner with Manchester United went on to state serious improvement is necessary if they are to stand a chance of winning Europe's premier club competition.
"If you remember from the last game when they beat Paris Saint-Germain [in the quarter-finals], all the interviews from the manager and the players were the fact that they created history, so maybe the mindset was 'we've gone as far as we can go'," Keane told ITV.
"They have made good progress over the last few years in getting to the semi-final but the next step, the big one, is trying to get to the final.
"We have seen over the two legs that they are still well short. They needed their big players to perform tonight and they never turned up."