The 32-year-old midfielder has been subject to some hefty and high-profile challenges this season with the last one of the Ladbrokes Premiership campaign coming on the final day at Parkhead on Sunday.
In the second half of the 1-0 win for the visitors, Shinnie picked up a yellow card for a foul on Brown which left him hobbling.
The Celtic captain was seen having words following the final whistle with Shinnie who, speaking after the game about the challenges in the match, said: “what comes around goes around”.
In response, Brown, who picked up his Ladbrokes Premiership player of the year award at Lennoxtown, said: “It will take more than him to put me down. I had a wee chat, that was it.
“There has been a few attempts. People want to win. Graeme makes a late, late tackle and you can see why he is on 16/17 bookings this season.
“It has been a fantastic season. To play 60 games every season, let’s see how long I can do it for.
“I feel fit as I ever have done.
“I have stayed injury-free, lucky enough for me, there has been a couple of dodgy tackles here and there but I have managed to get through them and continue playing.”