The 20-year old Brazilian, who arrived at Anfield from Inter Milan for £8.5million last month, added the Reds second goal early in the second half as they came away with an enormous victory over a disappointing Swans outfit.
Liverpool boss Brendan Rodgers says the club has high hopes for Coutinho and expect him to be a key player on Merseyside once he adjusts to Premier League football.
"He is a really talented player. He's only 20 but he's had good experience of playing at the highest level,'' he told Sky Sports.
"He'll take a bit of time to adapt to the whole tempo of the English game as he's come from Italy where the game is a little slower.
"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.''