Sterling, 23, has been in exceptional form for Manchester City this season with six goals and five assists in the Premier League, and is reportedly soon to be rewarded with a new contract worth close to £300,000 per week.
Speaking on 'Monday Night Football' as he covered stats showing only Mohamed Salah had been involved in more goals than Sterling the start of last season, Carragher claimed the winger deserves a pay rise.
"We are hearing reports that Sterling is on the verge of signing a big contract and maybe there are eyebrows raised because of the figures involved, but when you look at the stats, he is in the company of players who are earning those figures and people are saying are the best players in the league.
"Go back to England in the summer and this lad gets far too much criticism. When you look at what this lad is achieving, the move to Manchester City, the pressure and the price-tag. Plus Pep Guardiola, who everyone wants to play for, came in and can get players from Spain and anywhere in the world.
"This young English lad is thriving under maybe the best manager in the world and in the best team in the league. He deserves everything he gets.
"On the back of the Spain game against England [in which Sterling scored a brace], hopefully we will see a bit more of that because he does need to up his stats in terms of goals and assists for the national team.
"What he is doing for Manchester City now… we always talk about Sergio Aguero, David Silva and Kevin De Bruyne, but he is now in that company."