The BT Sport pundit has spoken of the pressure on the Ibrox manager, especially after the 1-0 loss to rivals Celtic in the Betfred Cup final.
Sutton has previously predicted that either Gerrard or Parkhead boss Neil Lennon will be sacked at the end of the campaign.
“If I’m honest, the team that finishes second in the league... I don’t see their manager lasting to next season. It’s that big,” he said.It is something he has reiterated in a Rangers context, nothing that the pressure and expectation that comes with the job means trophies have to be one.
He said: "The domestic pressure as manager of Celtic and Rangers is so extreme, the support that both clubs receive is unbelievable. Therefore, there are demands to win the title and we know the managers will come under scrutiny if they don’t deliver.
"Rangers manager Steven Gerrard will know this. Rangers have improved but you can’t go two seasons without winning something.”
Meanwhile, Sutton, who talks the Scottish game up when it's knocked by people in England, has been delighted to see the Old Firm doing so well in Europe despite their difficulties in terms of competing financially.
“A lot of people don’t know Scottish football, don’t understand Scottish football," he said. "The league gets humiliated! The worst team in the Premier League gets over £100m if they get relegated. So, when Celtic and Rangers football fans head into Europe, they want to see their team compete, but it’s not a level playing field.”
“It was a huge night for them against a good team to qualify. Celtic’s first win in 13 attempts on Italian soil so fair play to them. The Scottish league gets a real kicking so it’s good to see both Celtic and Rangers doing well in Europe this season.”