The captain and talisman finally prized open the Swiss defence deep into extra-time, two minutes from penalties, and picked out Angel Di Maria for the game's only goal. (Agencies)
And he said that the nail-biting win, in front of tens of thousands of Argentine fans, could stand his team in good stead later in the tournament.
"Suffering, suffering that's what I felt, but now we know we can go through times like this," said Messi.
"We were lucky, we had luck on our side and now we have to take advantage of it and move on."
Argentina will now play Belgium or the United States in the quarter-finals on Saturday, as they go for a third World Cup title on the soil of arch-rivals Brazil.
"Just like everyone else, I imagine, at times I was nervous because we couldn't score a goal and any mistake would have put us out of the World Cup," Messi said.
"We didn't want penalties and so we wanted to win it in extra-time.
"For the goal I thought maybe I should take a chance. And then I saw Angel on the right and I passed to him and fortunately we were able to score."
The Barcelona star was named man-of-the-match for the fourth successive time by online voters, ahead of Di Maria who had 10 shots on target - more than the entire Swiss team.
"I don't know whether I deserve this one (award) or not but what's important is that we've made it to the next stage, which is what we wanted," Messi said.
The captain and talisman finally prized open the Swiss defence deep into extra-time, two minutes from penalties, and picked out Angel Di Maria for the game's only goal.