The sign was seen by many as an insensitive play off the "Boston Strong" slogan that the Bruins' home town adopted in the wake of the recent marathon bombings.
"Last night's sign, to me, had nothing to do with hockey," Julien said after practice Tuesday. "Boston Strong is about something that struck our city, not our team. Maybe it's a little sensitive for the Boston people.
"Those kind of things happen in playoffs. Unfortunately the best and sometimes the worst comes out of the passion of our game."
The Bruins coach also referred to a Leafs fan who was reportedly assaulted as he left a game at Boston's TD Garden, calling the incident unfortunate.
Boston defeated Toronto 5-2 Monday night to lead the best-of-seven series two games to one.