White exited the game in the first quarter when he inadvertently collided with teammate Marcus Smart as he bent over to pick up the ball after P.J. Washington attempted a steal.
The collision led to White falling to the ground, clutching his head and neck, with the Celtics later ruling him out of the game with a "neck sprain".
"He's good," Mazzulla told reporters. "I haven't gotten a report back but he's OK, I spoke with him in the locker room."
In White's absence, Malcolm Brogdon played 31 minutes off the bench, contributing 30 points on 11-of-17 field-goal shooting with three rebounds and three assists.
The former Indiana Pacers point guard, who joined the Celtics in July, has added good scoring output lately, averaging 20 points over the last five games.
"It obviously changed our rotation as we were a man down, but I thought Malcolm was great tonight," Mazzulla said.
"He's a guy that is adjusting to playing on our team. He shows tremendous humility and patience. Tonight was big for him. He really helped our team and was really selfless. I'm happy for him."
MVP candidate Jayson Tatum led the way for the Celtics, who recorded their sixth straight win to improve their NBA-best record to 32-12, with 33 points.
Tatum scored 17 points in the third quarter as the Celtics responded to a 66-62 half-time deficit, to lead by 10 at the final change.
The Celtics small forward shot 12-of-27 from the field with four triples along with nine rebounds and six assists.
Mazzulla praised Tatum, who is learning how different teams are guarding him to develop his consistency.
"He's done a really good of developing an awareness, because it changes night to night and quarter to quarter," Mazzulla said. "He's done a nice job of building an awareness to what the coverage is and having a solution for that."