The Blancos have been eliminated in the last four of Europe's premier club competition for the last three campaigns, at the hands of Barcelona, Bayern Munich and Borussia Dortmund.
Those defeats have elongated Real's quest for a 10th European Cup success but Alonso says the painful memories will act as an incentive for Carlo Ancelotti's men to reach this season's final in Lisbon on May 24.
"In recent years, playing for Real Madrid, being knocked out of the semi-finals of the Champions League was very painful," the Spanish international told Club del Deportista
"That is why our aim is to reach the final this year and put those defeats behind us."
Real have began this season's competition in fine form, winning five of their six Champions League Group B games to set up a last 16 clash with German outfit Schalke.