The Serbian midfielder has struggled to live up to his billing since a £20m summer move from Benfica and has started just four games in all competitions.
The 20-year-old himself has previously admitted that he needs more time to settle in with the Reds, and Pascoe is certain that the youngster will ultimately prove his mettle.
"Lazar will definitely come good, he's a quality player," he told The Liverpool Echo. "That's why we brought him in here. He's working hard. He stays behind after training to do extra shooting.
"That's the kind of guy he is. He wants to do well and he's a winner. We've had a lot of new players coming in and it takes time for them to all gel together. But they are all quality players and will fit in fine.
"It is just that time where they have to bed in. They are training and working hard. Just give them time and then you'll see the best of them."
Markovic is expected to start Tuesday's Capital One Cup clash with Swansea City at Anfield.