The 34-year-old was pulled in Game 5 of the Bruins' second-round series vs. the New York Islanders with the team up 4-2 due to injury concerns.
The 2013–14 Vezina Trophy winner proceeded to start a must-win Game 6, giving up four goals on 27 shots in Boston's 6-2 loss to New York that saw them eliminated from the Stanley Cup Playoffs.
Overall, he posted a 2.36 goals-against average and a .919 save percentage through 11 post-season starts.
Rask's eight-year, $56-million contract with the Bruins expires in the off-season, making him an unrestricted free agent, but the Finn said he wants to stay in Boston.
"I'm not going to play for anybody else but the Bruins. This is our home," Rask told reporters, per Boston Hockey Now's Joe Haggerty.
"We have three kids with friends in school. I don't see any reason to go anywhere else at this point in my career."