Tom Coughlin's side allowed the 31-year-old to leave the club during free agency and Tuck signed a relatively low-cost deal with the Raiders, much to the bemusement of Giants supporters the defensive lineman has met.
He told the Newark Star-Ledger: "To answer your question, I am still surprised I'm not a New York Giant. The only thing weird is when you see Giants fans who have a tendency to tell you how stupid [the team] is.
"Those are their words, not mine. But yeah, it was weird. You spend nine years in one place. You have a lot of success there and a lot of great friends.
"So yeah, it's going to be weird but I understand the business side of things and you need to move forward."
Tuck recorded 63 tackles, 11 sacks and one interception for the Giants in the 2013 season.