Borini moved to Anfield from Roma this summer and the Italian's manager believes that the 21-year-old has the right mentality to succeed in the Premier League.
Rodgers said: "Expectancy is what comes from being at a big club so you have to deal with it both as players and manager.
"He is not alone. When you come to a big club there is always big expectation and pressure.
"This is a kid who works well and works hard and he will come good there is no question about that."
Liverpool host Premier League champions Manchester City on Sunday.