Jonathan Bernier made 31 saves for the Red Wings (5-13-3), who have lost 14 of their past 17 games.
"I thought our battle level was about 80 percent, and if we're not close to 100 percent, we're not giving ourselves chances to win games," Detroit coach Jeff Blashill said. "There are teams in this league that can be at 80 or 85 percent and win games because they score so easily. We're not that kind of team."
The Red Wings, who were shut out for the second time in four games, have gone 13 games without a power-play goal. They were 0-for-1 with the man-advantage.
Detroit will host Nashville again Thursday.
"In this league, it is so important to score goals on the power play because it is so hard to score 5-on-5," Red Wings captain Dylan Larkin said. "We took a couple penalties in the third period and they scored, but you can't win hockey games without generating offense. We have to find ways to score goals."
The Predators appeared to take the lead when Forsberg scored at 16:54 of the second period, but the Red Wings successfully challenged for goalie interference.
Forsberg did give Nashville a 1-0 lead on a power play when his shot deflected off Red Wings defenseman Marc Staal for a power-play goal at 4:36 of the third period.