They'll try to find offense elsewhere again Friday night when they host the Colorado Avalanche, one of the best defensive teams in the NHL.
Parise, who leads the Wild with 22 points, skated before Wednesday's 3-1 loss to Phoenix but is expected to miss at least two weeks with a bruised foot suffered in Monday's 3-0 defeat in St. Louis.
The Wild (15-7-4) are hoping to avoid losing three straight in regulation for the first time this season.
They also lost center Mikael Granlund against the Coyotes and placed him on injured reserve Thursday with an upper-body injury. Jason Zucker was recalled from AHL Iowa.
"It seems like every game right now we've got different guys going out with different guys. But there's no excuses," coach Mike Yeo said. "That game was still there for us but we've got to make sure we're ready to start better, that's all."
Dany Heatley scored midway through the third period to get the Wild within a goal, but they weren't able to tie it before Phoenix's empty-netter in the final minute.
"We're not coming out with the same force in our game, like we're going to dictate and take control," Yeo told the team's official website. "We're very reactive, on our heels. We're going out there and trying to be safe. When we're at our best, we're playing an aggressive game both with and without the puck."
Niklas Backstrom made 23 saves in his third start since coming off injured reserve. He's 6-0-1 in his last seven against the Avalanche and 26-9-3 in his career, which accounts for the highest win total he has versus any franchise including the playoffs.
The Wild went 4-0-1 against the Avalanche last season and are looking for a fourth straight win against their new Central Division foes.
The Avalanche (17-6-0) haven't been much better than the Wild lately in the offensive zone with two goals in two games.
They lost 4-1 to the Blues on Wednesday to match their worst home defeat of the year. St. Louis scored twice in the opening 6:10 and led 3-1 after the first period.
"We lost the game in the first 10 minutes," said center Matt Duchene, who returned from a three-game absence due to an oblique strain. "If we played a little better in the first 10 there, even giving up that (short-handed goal) late in the first period there we go into the next period with a 2-1 deficit, it's a different game."
While the Avalanche got their leading scorer back in Duchene, they played without Paul Stastny, who sat out with back spasms and could miss Friday's game. Stastny leads Colorado forwards with a plus-10 rating.
Duchene has team highs of 12 goals and 20 points. He has five points in his last four games against the Wild.
The Avalanche have the sixth-best goals-against average in the league at 2.13 and have been particularly good on the road. They're a league-best 8-2-0 away from home with an NHL-low 1.80 GAA.