It was ultimately too deep of a hole for the Bruins, despite their comeback effort.
Boston has three games left and is one point behind the Philadelphia Flyers for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. The Bruins are also one point behind the Detroit Red Wings for third place in the Atlantic Division.
The Bruins conclude the regular season with three straight home games against the Carolina Hurricanes on Tuesday, Red Wings on Thursday and Ottawa Senators on Saturday.
"This time of year, with what's at stake, we have to be a lot better," Bergeron said. "The focus is definitely what cost us the game early on, by making some mistakes and giving them the space that they wanted and making the plays that they wanted. It's definitely not an excuse, with how many games left and what we're looking at standings-wise."
Scott Darling started his ninth straight game for the Blackhawks and made 42 saves. Defenseman Brent Seabrook had two assists for Chicago, which split the season series with Boston after losing 4-2 at TD Garden on Mar. 3.
Chicago played its second of six games without suspended defenseman Duncan Keith, a two-time Norris Trophy winner, and lost right wing Marian Hossa in the third period. Hossa limped off the ice after a collision in the neutral zone and didn't return.
"He seemed to be OK [after the game]," Quenneville said. "We'll know more [Monday], but we don't think it's much. Hopefully he'll be fine and ready to go on Tuesday [against the Arizona Coyotes]. We'll know more [Monday]."
Prior to the game, the Blackhawks and Bruins honored linesman Andy McElman with a ceremony to commemorate his retirement. McElman, who's from the Chicago area, finished his NHL officiating career by working his 1,500th game.