Boston, with 88 points, remained in third in the Atlantic Division; it has a one point lead on Detroit, which has lost three of their past five games. Each team has five games remaining. Boston plays its next two on the road against the St. Louis Blues and Chicago Blackhawks.
The Red Wings and Bruins play at TD Garden on April 7.
"We [have to] play for our lives," Julien said. "It's our own fault if we make it harder on ourselves all the time. Obviously when you look at the way the game went, the game plan was good, but the part that we can't help them with is the finishing part and that's what we [have to] get better at."
The Bruins have scored 10 goals on 238 shots (4.2 percent) and are 2-for-19 (10.5 percent) on the power play in their past seven games. Three of the goals, including each power-power play goal, came in their 3-1 win at the Toronto Maple Leafs on Saturday.
"Like we've been talking about a lot lately, it's about bearing down, scoring, finding the back of the net," Bruins center Patrice Bergeron said. "When we do have a power play we have to do the job. When we're on the PK, same thing. We've got to be better. At this time of the year, having chances is not good enough."