The team were defeated in extra time in their round-of-16 clash against Argentina yesterday, bringing the 65-year-old's 31-year coaching career to an end.
Haris Seferovic told FIFA.com: "He's a wonderful person and we all respect him a great deal. Even when he names me as a substitute, I always remind myself that he knows what he's doing. We owe him so much. He brought about a big change and built the team around us younger players."
Granit Xhaka added: "He put together a really good team that will last for many years to come."
Meanwhile, Josip Drmic simply said: "He's done a great job."
Hitzfeld, who was in the dugout for last night's match despite his brother's death the day before, had been in charge of Switzerland since 2008.