The England international is on the verge of agreeing a new five-year deal at City that will see him earn £300,000-a-week, becoming the highest-paid British player in the process.
Carragher said: "Raheem Sterling is on the verge of signing a really big contract and maybe eyebrows raised at the figures involved.
"But he is in company of players who are earning those figures. This lad gets far too much criticism.
"What this lad is achieving, the move to City, the price tag, Guardiola coming in. A young English lad is thriving in a team with maybe the best manager in the world.
"He deserves everything he gets. What he is doing for Manchester City now, we talk about Aguero, Silva, De Bruyne; he is in that company."