Curry injured his foot after Smart dived for the ball in the second half, crashing into the two-time MVP’s leg and leading him to limp out of the game.
Warriors coach Kerr, who was visibly upset after the incident, called it “dangerous play.”
“I thought Marcus dove into Steph, and that’s what I was upset about. A lot of respect for Marcus,” he said.
“He’s a hell of a player, a gamer, a competitor. I coached him in the World Cup a few summers ago. We talked after the game and we’re good. But I thought it was a dangerous play,” he added.
Curry underwent an MRI after the game. Meanwhile, Smart said he was just going for the ball and hadn’t seen Curry.
“Me and Steve have a relationship from USA basketball, so he knows I’m never trying to hurt anybody. I hate to see any injury. I hope Steph’s alright.
“I didn’t even see him, I just dove on the ball and tried to make a play. I’m really down right now about it.
“Unfortunately, sometimes, injuries happen. I’m sure I’m going to get called dirty. That’s their opinion,” he added.
Meanwhile, Warriors forward Moses Moody saw only nine minutes of play before leaving the first half with a shoulder injury.
Jayson Tatum had 26 points and 12 rebounds and Jaylen Brown added 26 points — with over half of those in the first half — to help lead Boston.
After enduring five separate, multi-game losing streaks in the first two months of the season, the Celtics now haven’t lost back-to-back games since January 19-21.
“All night, we were physical, from 1 to 15,” said Brown.
“We were into guys, trying to ride them out, not letting them get space, not letting them feel comfortable, and that’s what we want to do. We want to be the aggressor, and I think we did that tonight.”
Celtics’ head coach Ime Udoka said: “You obviously look at the results, 17, 15, 19 in the first, second, and fourth quarter, so other than that third quarter, I felt our physicality was great.
“Any time we can impose that on guys from the start, we wanted to do that and start the road trip off right.”
The Warriors will host San Antonio Spurs on Sunday, while Celtics will take on the Sacramento Kings on Friday.