Angel di Maria struck a dramatic 118th-minute winner after normal time was not enough to separate both nations in Sao Paulo today.
Hitzfeld, whose brother passed away just hours before kickoff, praised his players for their contribution but says that he will now call time on his 31-year coaching career in order to pursue a "quieter life".
"I'd like to congratulate my players for the way they reacted at the end," he told FIFA.com. "Today Switzerland earned the recognition of many people around the world and we can walk away with our heads held high.
"As for my future, I'm retiring from coaching so I can lead a quieter life."
On Monday, the 65-year-old claimed that this evening's clash would not mark end of his career.
Hitzfeld took charge of the Swiss national team back in 2008 and recently guided them up to sixth in the FIFA rankings following an unbeaten World Cup qualifying campaign.