Messi set up Angel di Maria's 118th-minute winner as Argentina edged past Switzerland 1-0 in their round of 16 clash at the Arena de Sao Paulo.
Blerim Dzemaili almost forced penalties after Di Maria's goal, hitting the post with a header and poking the rebound wide.
Messi said his team were desperate to avoid a shootout and wants them to capitalise on their slice of luck as they prepare to face Belgium in the quarter-finals.
"Like everybody I was very nervous because we couldn't score. We knew if we made a single mistake we would have been going home," he said.
"We didn't want it to go to penalties. We suffered, suffered and suffered, all of us. We started to think it wasn't going to happen.
"But at the end we had luck on our side and now we have to take advantage and move on."
Messi had scored in each of Argentina's three group games for a total of four goals, and the Barcelona star considered taking the late chance on himself.
He was released into space after a Switzerland turnover on halfway, but said he spotted Di Maria's run just in time before the Real Madrid attacker finished clinically into the bottom corner.
"When I first got the ball I thought about taking the chance and shooting myself, but then I saw Angel and made the pass," Messi said.
"Fortunately we were able to celebrate. What's important is that we went through. So many big teams have already gone home."
