World champions France were sensationally bundled out after leading 3-1 with 10 minutes to play, with the Swiss rallying with two late goals from Haris Seferovic and Mario Gavranovic.
Goalkeeper Yann Sommer was the hero in the shootout, denying Kylian Mbappe in the decisive moment as Switzerland progressed 5-4 on penalties.
“I’ve always said this team deserved a lot more than you can read,” Xhaka told the post-match media conference.
“There was so much discussion about this team. They said we were arrogant but I can guarantee you one thing, we really wrote a history.
“All Swiss people can be really proud. We achieved something that is impossible to describe with words.”
Switzerland had led 1-0 at half-time after Seferovic’s opener, before seeing Ricardo Rodriguez’s penalty saved by Hugo Lloris.
France rallied from there, with Karim Benzema netting a double and Paul Pogba making it 3-1 with a stunner before the late Swiss twist.
“I had a positive feeling and in my opinion we played a perfect first half,” Xhaka said.
“Then we missed a penalty and conceded three goals. This was a slap in the face but we committed mistakes.
“But that we still turned it around against a team such as France, with all the top players in their ranks, is just unbelievable.”