Dylan Larkin scored twice for the Red Wings in the first period and Tyler Bertuzzi added a power-play goal in the third. Larkin and Andreas Athanasiou both buried their shootout attempts against rookie goaltender Jonas Johansson, who made his first NHL start for the Sabres.
The loss is Buffalo's fourth in five games since returning from the All-Star break, a string of poor results that Krueger feels has impacted their offense.
"When you just purely look at the game from scoring chances as we do as coaches, there is an effort to get the job done," Krueger said. "There is a lack of confidence right now, so what you're seeing sometimes is hesitation on scoring chances. You're seeing hesitation on puck movement when it can be a little bit quicker. But I do not see these guys quitting.
"I think there's a bite in that room. They don't want this season to fall away. They want to fight against this storm that we're fighting against right now and we have to stick together, and we have to work together on solutions. That's all we can do in this adversity right now."
The Red Wings took an early lead on a goal from Larkin, who utilized a screen from Luke Glendening and beat Johansson with a shot from the half wall. Larkin added another goal with two tenths of a second remaining in the period, the product of a 2-on-1 rush that was born out of overly aggressive play by the Sabres at the other end of the ice.
Vesey buried his own rebound to put the Sabres on the board at 5:48 of the third period, then Wilson deflected a shot from Colin Miller to tie the game less than three minutes later.
Rodrigues took the high-sticking penalty that preceded Bertuzzi's go-ahead goal but redeemed himself after Rasmus Ristolainen made an aggressive play to poke the puck free with the Buffalo net empty in the final minute. Rodrigues cut quickly through the middle of the ice, collected the puck and scored.
It was the last puck they got behind Red Wings goalie Jonathan Bernier, who stopped Jack Eichel and Sam Reinhart in the shootout.
"We had moments in the first and second that were positive and we did the right things, but we didn't do it consistently enough," Rodrigues said. "We waited too long to turn it on. We fought our way back and unfortunately don't get the two points, but we had chances and it didn't go our way tonight."