The legendary Celtic captain left the club at the end of the 2020-21 campaign and while the Glasgow outfit went on to win the cinch Premiership last term, Sutton still feels Brown has not been adequately replaced.
Writing in his Daily Record column, Sutton said: “It was pretty difficult to pick holes in the way Celtic went about their business last season. There were so many good aspects, so many exciting sights.
"However, if there was one thing that I wondered about, it was physicality. I felt that, in certain circumstances, it would have helped them.
“Postecoglou wants to play a certain way and I think we all admire that.
“Get on the front foot and play the game you want. Don’t take a backward step.
“However, there are times in games when you don’t intend to take a backward step, it just happens.
“You get pushed back and you need people to hold firm.
“Celtic ’s attacking style leaves their centre-backs exposed.
“Most of the time, you can cope with that but not in Europe. In the Europa League, Postecoglou’s team were picked off time and again in the groups and lost five over two legs to Bodo/Glimt in the Conference League.
“There were times when it seemed Callum McGregor, as well as trying to make passes and keep the game ticking in one direction, was having to try and cover in front of his central backline by himself as waves crashed against him in the other.
“Nir Bitton has now gone and, when I think of Celtic going into the group stages of the Champions League, they are going to need someone to help hold the fort in the middle of the park.
“Given the way Postecoglou wants the game to be played, that’s a challenge for him and his recruitment staff.
“The Aussie isn’t just going to want a bruiser in there who just kicks people, makes tackles, covers runners but can’t pass the ball.
“He’ll want someone who can play as well as do the ugly side to a high level and, in the modern game, prices for these fellas can range up to around £50million.
“Finding that diamond in the rough, as they did with Wanyama, is the task. I see Brazilian Vinicius Souza is one name mentioned for the role, so it seems they are looking.
“I feel it’s a must. Bitton did an admirable job playing that position and there is no-one else like him in there with his stature and presence.
“Ismaila Soro isn’t the answer and you wonder if Yosuke Ideguchi might be able to.
“He’s not yet had a chance to flourish and, although he’s not the same as Bitton physically, neither was Neil Lennon or Scott Brown and they still managed to scavenge around putting out fires and dealing with danger to protect their centre-halves.
“Nonetheless, whether it is to anchor alongside McGregor and push him one up, Celtic need to source one because the rest of the midfielders are the same, if not in shape or size, but in style.
"In my Celtic days it was Neil Lennon.
“Subsequently, it was the likes of Scott Brown and Victor Wanyama who did the job.
“It takes different pieces to fit a puzzle and, for all Celtic’s attacking quality, Ange Postecoglou will be aware you need balance.
“And I’m convinced the Hoops could do with getting an enforcer in the door.