The Brazilian midfielder, who joined from Inter Milan last month, scored on his full debut as the Reds ran out comfortable winners at Anfield.
"He'll take a wee bit of time to adapt to the whole tempo of the English game," Rodgers told the club's official website. "He's come from Italy where the game is a little slower but he's a wonderful technician.
"You saw the quality and the speed of his passing all game - he's got wonderful game-knowledge. I've got high hopes for him."
Sunday's victory has moved Liverpool up to seventh place in the Premier League table.