The simple answer is that it was not transported to Constantinople, a city that was not called that in 33AD, which was not dated that, in 33AD, and that the travels of the Shroud are cloaked in mystery for much of its existence but that there are reliable reports of a cloth with an image of Christ under different names that have been described from at least the 2nd Century, when it was known as the Mandylion, the Image of Edessa, and even myths and rumors from even earlier. There is a gap from the 2nd Century to the 6th that is explained by it having been sealed in a wall in Edessa, Turkey, to protect it from Iconoclasts before it was re-discovered in an earthquake that destroyed the wall in 525 AD.
The simple answer is that it was not transported to Constantinople, a city that was not called that in 33AD, which was not dated that, in 33AD, and that the travels of the Shroud are cloaked in mystery for much of its existence but that there are reliable reports of a cloth with an image of Christ under different names that have been described from at least the 2nd Century, when it was known as the Mandylion, the Image of Edessa, and even myths and rumors from even earlier. There is a gap from the 2nd Century to the 6th that is explained by it having been sealed in a wall in Edessa, Turkey, to protect it from Iconoclasts before it was re-discovered in an earthquake that destroyed the wall in 525 AD.