Liverpool splashed £35million on Oxlade-Chamberlain in August, signing the 24-year-old from Premier League rivals Arsenal.
However, the England international has endured a torrid start to his Reds career, helping Jurgen Klopp’s side win just once since his arrival.
His campaign hit an all-time low in midweek when he was criticised for a dreadful performance in England’s unconvincing 1-0 victory over Slovenia.
And Celtic legend Sutton thinks Sinclair deserves a chance to shine, having hit 35 goals from 66 appearances since signing from Aston Villa in the summer of 2016.
“Alex Oxlade-Chamberlain has had a torrid start to the season,” he told the Daily Record.
“His confidence is through the floor, yet he’s back in the fold.
“Gareth Southgate’s approach towards Scott Sinclair smacks of arrogance. If I was Sinclair, I’d be most unhappy. It’s a public slap in the face and it was unnecessary.
“Actually, it was just downright dismissive towards Scotland.
“If that was an English Premier League player, I’m pretty sure the response would have been along the lines of: ‘I’m aware of him, he’s in my thoughts. It wasn’t to be this time, but if he keeps working hard, we’ll be aware of it.’”
Sutton’s comments refer to Southgate’s words about Sinclair last week, where he suggested the ex-Manchester City winger was not good enough for his Three Lions squad.
“I had a conversation with Brendan (Rodgers, Celtic boss) about him at the end of last season,” Southgate said.
“He’s a good player but we have good quality in that area of the pitch and at the moment I think he is just below the level of what we have already got.”