After Dragosin went off injured in the 87th minute of the 1-0 defeat to Forest, Spurs finished the game with 18-year-old Archie Gray filling in at the defence, and fellow midfielder Yves Bissouma in the centre-back roles.
Full-back Jed Spence will also be suspended for the 15:00 GMT kick-off against Wolves, with Postecoglou saying the injury crisis is the worst he has faced in his managerial career.
He added: “There have always been problems at different times, but not to this extent.”
“I think we had about 10 first-team players unavailable for a long period of games.
“We've been through this for a long time, and we haven't had any other problems, but the nature of football and the scheduling that we have, we've always been on a good streak.” Of the ability to pass.
“It's another test for us, but that's what it is, whatever we have to deal with, we'll deal with it and get ready for Sunday.”
Forest's defeat was Tottenham's ninth of the season and left them 11th in the Premier League.
The team will play Liverpool in the Carabao Cup semi-final next month, and Postecoglou said he still feels the support of the club's fans despite the increasing pressure and criticism of his attacking style.
“They love their football club, they care about their football club, and they want their football club to succeed,” the Australian said. “They make those feelings and emotions visible.
“I haven't felt anything but support since I've been here. I still feel the support is there. I will continue to do what I believe is the right thing to bring success to this football club, and that doesn't change.”