The Belgian has been expected to leave Parkhead in recent weeks after a wealth of interest from England, Spain and Turkey this summer.
Boyata had not featured for Celtic since returning from the World Cup, claiming he was not fit enough to be included in Rodgers’ first-team squad.
However, the former Manchester City defender started against Hamilton, before scoring the only goal of the game to get the Hoops back on track.
And skipper Brown admits Boyata and Rodgers have cleared the air in recent days.
“What’s said at Celtic Park and Lennoxtown stays at Celtic Park and Lennoxtown,” he said.
“But it cleared the air. Of course it did.
“We are just looking forward to Thursday now.
“We want to get into the Europa League.
“Then we’ve got a big game on Sunday before the international break.
“So, they are two big games for us and we need two victories to put a smile on everybody’s face.”
A section of Celtic fans jeered Boyata throughout the clash on Sunday afternoon.
And a banner was unfurled in one of the home stands, reading: “Boyata – not fit to wear the jersey.”
But Brown refused to be drawn on the supporter gesture, claiming he didn’t see the banner.
“I didn’t see it,” he added.
“We are all together and that’s the main thing for us.
“It’s been a hard week for him but it’s fantastic at the end of it.
“He’s scored the goal and got us the three points we deserved.
“I’m pleased for him – it shows his character.”
Speaking after the clash, Hamilton captain Darian MacKinnon said: “It was a mad experience out there, with the banner and were fans booing and cheering Boyata.
“Listen, nobody knows what was really going on. Boyata’s a professional player, you don’t know if he’s been injured.
“That’s down to Celtic’s business, obviously.
“But, you saw today what a top player he is, and it was just unfortunate for us this was his first game back.
“We gave it everything and we just came up short. We did well, our shape was good. The only disappointing thing was losing a goal from a set piece. If they’re going to beat you then you want it to be a wonder goal.
“That’s the only complaint we could’ve had on the day.”