The 20-year-old Brazilian joined the Reds from Inter Milan for £8.5m on Wednesday in what was described as a "long-term deal".
"He has played a lot of games from a young age," said Pascoe. "What we have got there is a young talent who has played a lot for Inter Milan and Espanyol.
"He is a young lad but what we have seen of him he can handle this type of pressure and he will be a good asset for us.
"The young lads who have come through have been absolutely brilliant but he has a lot of experience."
Coutinho has been ruled out Sunday's trip to Manchester City in the league with a hamstring strain.