Aston Villa turned his loan into a permanent deal this week when they agreed to pay a fee of £17m to Barcelona and Coutinho has also agreed to take a massive pay cut to make the deal happen.
The Brazilian made a bright start when he joined the Midlands club in January, but since then his influence has been fading and he has not registered a goal or an assist in his last nine appearances in the Premier League.
Liverpool are hoping that Aston Villa boss Steven Gerrard and Coutinho combine to stop Manchester City on the final day of the season and aid the Reds in their push to win the league.
But Lawrenson does not see that happening and stressed that Coutinho is not going to be a factor against the top sides in the Premier League.
He insists that he hardly noticed him when Liverpool beat the Midlands club at Villa Park last week.
Lawrenson said on Off The Ball: “I was at Villa Park on Tuesday and Coutinho, to be honest, I didn’t really see him.
“The game passed him by a little bit.
“Coutinho against any team outside the top six will be outstanding because you will get a bit more of the ball and he is very good with it.
“But against the big teams, I just felt he is a little bit of a non-entity.”
Coutinho did score against a top team on his debut for Aston Villa when he netted in a 2-2 draw at home against Manchester United.
