Swansea are bottom after four straight defeats but victory over Palace would lift them to 18th and within a point of their opponents, whom they beat 5-4 last month.
"It's an important game for us and a chance to get three points," Barrow told swanseacity.net. "Today we knew it wasn't going to be easy, but Swansea we have to come away with the three points.
"It's very difficult. It's not easy, but being in England we know what to expect."