The Wings had just a 6.7 percent chance of getting the first overall pick, which did not happen, even with Kris Draper in Toronto representing the team.
The Wings ended up in ninth, pushed down two places.
The lucky teams ended up being the New Jersey Devils, Philadelphia Flyers and the Dallas Stars.
The Devils will pick first for first time since 1979, moving up from fifth.
The Flyers jumped up from 13th to second. It will be the second time in their history the Flyers have chosen second. They took James van Riemsdyk second in the 2007 NHL Draft.
The Stars moved up to third, gaining five spots.
The last time the Wings selected in the top 10 was when they selected forward Martin Lapointe with the 10th puck in 1991.
The last time they chose a player ninth was defenseman Willie Huber in 1978.
Huber played 12 seasons, five with Detroit.
The Colorado Avalanche, who had the best chance of winning the lottery, ended up fourth.
The NHL Entry Draft will take place June 23-24 at the United Center in Chicago.
This is the order of the top 15 picks, with the rest to be set following the playoffs:
1. New Jersey Devils
2. Philadelphia Flyers
3. Dallas Stars
4. Colorado Avalanche
5. Vancouver Canucks
6. Vegas Golden Knights
7. Arizona Coyotes
8. Buffalo Sabres
9. Detroit Red Wings
10. Florida Panthers
11. Los Angeles Kings
12. Carolina Hurricanes
13. Winnipeg Jets
14. Tampa Bay Lightning
15. New York Islanders
