The Bayern Munich man scored in the sixth, 31st and 71st minutes in Manaus on Wednesday, to send Ottmar Hitzfeld's men into a last-16 date with Argentina.
Shaqiri opened the scoring at the Arena da Amazonia with a pearler from range, before Josip Drmic twice assisted his team-mate to nurture him to the 50th hat-trick at a World Cup finals.
And the 22-year-old, who also pointed to his team-mates after goals two and three, said his feat was the result of a team effort.
"I wanted us to play football and we did that. I wouldn't have scored three goals without them," Shaqiri said.
"I'm very proud of my hat-trick; I'm never going to forget this but that said I'm more proud of us as a team and that we've qualified for the round of 16."
On their impending clash with Alejandro Sabella's side on Tuesday, Shaqiri said his team would be unfancied against a tournament favourite but was not giving up on his plucky side who qualified out of Group E with two wins.
"It's a dream – small Switzerland against Argentina. It will be a great match and we'll be ready for them," Shaqiri said.
"Although we're underdogs, anything is possible. You never know in football."
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