A dominating last period didn’t repair the damage of the first two, eventually going down 7-1.
The Brits can still get through to the finals if they win their next two games though.
Steelers goalie Ervins Mustukovs had warned about the risks attached to taking penalties - and four of the goals conceded came on the Power Play.
Clever, fast on the forecheck and super-skilled on the transition and not bad at face off - Minsk were good and home grown centreman Viktor Turkins with two goals and two assists was excellent.
Minsk, fast, big and well co-ordinated dominated centre ice in the mainly empty stadium in Rungsted, Denmark, and grabbed two goals in the first and eighth minute from Alexander Kogalev and Nikita Mitskevich.
A back hander from Dowd almost got Steelers on board but they took a penalty and Minsk’s crisp passing delivered again, Belarus international Turkin scoring with a one-time blast.
Minsk, a feeder team for the KHL giants Dinamo Minsk who were founded in the same year as Steelers in 1991, had a fourth scorer on the board through Konstantin Zackharov at 23;15.
Then Mustukovs rebounded a shot and Pavel Razvadovsky put it away for 5-0 (PP.)
A third PP goal of the afternoon from Marek Slovak ended a second 0-3 period.
Sheffield spent more time in the opposition zone at the start of the last session.
It was a relentlessly fast game of few stoppages - and it was enlivened by a good clean hit from Zack Fitzgerald and some aggression from Brady Ramsay and then a Power Play goal to avoid the shut out from Roy, assisted Matheson and Valdix.
Penalties against Marquardt and Fitzgerald near the end interrupted the offensive flow - and it was game over when Turkin struck again on the PP.
Attendance: 641.
*Steelers’ second game of the tournament is Saturday against the host club Rungsted. Thjey play Latvians Riga on Sunday.