The Danes drew 1-1 with the Slovenians before watching England notch a 1-0 win over Serbia, with Jude Bellingham getting the goal and Kane, Bukayo Saka and Phil Foden providing a stern test for the Serbian defence.
"If doubt starts to creep in, it could be a really long day, it's sometimes important to maintain a kind of confidence that some would call naive and blue-eyed," Vestergaard told broadcaster DR.
"We believe in ourselves - if we don't believe in ourselves, I don't think anybody else will," added the centre-back, who plays his club football for English side Leicester City.
Vestergaard will be keeping a particularly close eye on striker Kane, who played as a target man in the first half against the Serbs before dropping deeper in the second as the English defended their slender lead.
"He is a very complete striker who more or less has the whole package - he can play with his back to goal, he can make dangerous runs into the box, and he can threaten to go in behind," Vestergaard explained.
Regardless of how tough Thursday's challenge will be, the Danish defender said he is looking forward to it.
"He (Kane) is good at everything and that's what makes it hard to take something away from him, because then he just does something else," he said.
"So in that way it's hard to play against him, but it's also a fun challenge."