Madrid were given a huge scare in the second leg of their Champions League quarter-final clash as Dortmund scored twice through Marco Reus during a rampant first-half performance to cut the Spanish side's aggregate lead from 3-0 to 3-2.
Dortmund then saw Henrikh Mkhitaryan hit the post when faced with an open goal in the second half while Casillas was called upon to deny Mkhitaryan and Kevin Grosskreutz soon after as Jurgen Klopp's men pushed hard for an equaliser.
The German side could not find a third goal to keep their hopes of a famous comeback alive though, and a relieved Madrid were able to celebrate a spot in the Champions League semi-finals for the fourth successive season.
However, if they are to go any further, Casillas knows they cannot make the same errors that plagued them in Dortmund, which included big mistakes from Pepe and Asier Illarramendi for both goals and a missed early penalty from Angel Di Maria which helped galvanise the home side.
Casillas said: "We've had to suffer too much. Maybe it's good to have a wake-up call now and again and to realise things aren't easy.
"The errors at the back have made us suffer all game, but better in this game than in the more decisive ones in the next two weeks."
The Spain captain, whose side play Barcelona in the Copa del Rey final next week, added on his club's website: "The first goal was a mistake from us and the second was where we lost the ball in the middle of the pitch.
"We had mental strength because being 2-0 down in the 37th minute a lot of things go through your head and all this after missing a penalty.
"The positive thing is that we've learnt to suffer in these games. These errors cannot happen in the semi-finals."
On how Di Maria and Illarramendi were feeling after the match, Casillas said: "They aren't feeling great but this is a team and we've got through. You've got to give them every support and fight as a team."
Midfielder Luka Modric echoed Casillas' comments while admitting his side may have been guilty of a bit of complacency.
The Croatia international said: "We're happy to have got to the semi-finals but not for how we played tonight, especially in the first half.
"We cannot allow that and we need to improve. But the most important thing for us is getting into the semi-finals.
"It could be that we relaxed a little after winning the first leg 3-0 and were thinking in our heads that it was going to be easy. We need to learn from this game."