The 20-year-old, who signed from Inter Milan at the end of January, struck moments after the re-start at Anfield to double the Reds' advantage courtesy of a fine solo effort.
"Coutinho is a really talented player," Rodgers told reporters. "He's only 20 but he's had good experience of playing at the highest level.
"He'll take a wee bit of time to adapt to the whole tempo of the English game. 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. He's the type of player that we are trying to bring in here - a technician who has a strong character and good mentality. I'm sure he'll progress very well."