Hitzfeld will retire from football at the conclusion of the ongoing FIFA World Cup finals, in which Switzerland won their first game on Sunday.
Haris Seferovic's 93rd-minute strike gave Switzerland a thrilling 2-1 triumph against Ecuador to gain momentum ahead of a Group E clash against France on Friday.
Shaqiri could have a big say in his country's prospects of progressing to the last 16 and the Bayern Munich star said his team want to make Hitzfeld proud.
"Technically, we've improved a lot," Shaqiri told the Bundesliga's official website on Monday.
"(High expectations) are an honour, but also a burden. But it's pressure I can cope with very well.
"We'll be doing everything in our power to have a good World Cup and ensure the coach ends his great career on a successful note.
"We all get on very well with him. He's a great communicator and we've got an excellent working relationship going."
Hitzfeld was appointed Switzerland coach in 2008 and under his tutelage they have risen to sixth in the FIFA rankings.
They were knocked out in the group stages of the 2010 World Cup under Hitzfeld and failed to make UEFA Euro 2012.
Vladimir Petkovic will take over from Hitzfeld at the conclusion of the Brazil showpiece.
