The 22-year-old was named in Germany's 27-man preliminary squad for the tournament, but was one of four players cut when head coach Joachim Low announced his final panel on Monday.
After a season where he helped City to the Premier League title with 15 Premier League assists, Sane was expected to compete for a starting position in Russia, but Low had other ideas as he chose Marco Reus, Julian Brandt and Julian Draxler ahead of him in his squad.
The winger has played 12 times for his country, but failed to impress Low, providing just one assist and no goals in his international career so far. Despite this, many people were surprised by his absence, including Man City team-mate Kyle Walker and former Germany international Michael Ballack.
Sane posted in both English and German on his Twitter account, thanking all the people who had sent him messages following the shock announcement, while also vowing to continue to develop as a player and return to the national side.
"Thank you so much everyone for your encouraging messages yesterday and today," Sane wrote.
"I'm obviously very disappointed I won't participate in the World Cup, but I have to accept this decision and I'll give it my all to bounce back stronger!
"Nothing but the best of success to the DFB Team in Russia. Go get that title!"
As well as Sane, Low also cut goalkeeper Bernd Leno, defender Jonathan Tah and forward Nils Petersen from his initial 27-man list.
Leno also posted a message on his social media accounts, wishing the national team well at the World Cup whle also revealing his frustrations after being left out of the final selection.
"Of course I am disappointed," the Bayer Leverkusen goalkeeper wrote.
"I gave everything in the training camp for the big dream, but this is part of the sport - take setbacks, accept decisions and continue to give everything. Germany, I wish you every success in Russia."