The Bayern Munich star got a big chance to open the scoring in the dying seconds of Wednesday's encounter, but Mascherano's last-ditch tackle eventually prevented the Dutchman from finding the net.
The game went to extra time following Mascherano's interception and Argentina eventually booked their ticket for the final after penalties, with goalkeeper Sergio Romero saving two spot-kicks.
"Robben played a great exchange with [Wesley] Sneijder but, because of that extra touch, he didn't quite hit it so early, it gave me the possibility, that extra split second," Mascherano told The Independent.
"The team was lucky Robben took one more touch. To get to a final, you always need a bit of luck.
"It was a terrible moment. I thought I'd slip, I thought I wouldn't make it, I thought he'd get ahead of me. I thought so many things. But I did get there and it wasn't a goal.
"Anyone could have done it, but I was lucky to get there. The truth is there was not much doubt for me. I just threw myself into it. If I was a moment off, it was a penalty. There's no doubt."
Mascherano then went on to voice his delight with Argentina's successful World Cup campaign as they made it to the final for the first time since 1990.
"We did the things we had to do. We have the tranquillity of having given everything, of having performed like we had to. That forms part of this group.
"It's been so many years but now our country, and our flag, are in the eyes of the world, returning to a World Cup final, the most important match of our careers.
"It's a delight, a delight that lifts your soul. It's something you can't explain, something I never imagined, but there we are."