The Spanish keeper' saved Adelaide's penalty, the fourth in the shootout for Angers after the game finished 1-1 in normal time.
The French club opened the scoring through Farid El Melali before Reiss Nelson levelled early in the second half.
"When he was coming up to the penalty spot I was saying, 'Jeff, I know you, I know you so well'," Martinez told the club's website. "I was guessing the wrong side for the first three pens and I think for the fourth pen I forced him to miss because I waited so long for him.
"Penalty shoot-outs are one of my strengths, so I'm delighted to win today. I wanted to win against Real Madrid as well, but sometimes you win, sometimes you lose.
"The only penalty shoot-out I've lost in my career was against Real Madrid. I just look at myself and I know that I'm really good at it, so when I'm in a penalty shoot-out, I'm nice and relaxed because I know that I will at least save one or two.
"When I was on loan at different clubs, we literally studied the strikers, which side they went [for penalties] and what their strength was. I believe in my own strength, in my guessing and I just go for it."
"If I guess the right side, I've got a really push, so I only think about myself and I don't care about who I'm facing. I just guess and go for it."