Goals from Cedric van der Gun, Darren Pratley and Shefki Kuqi eased Swansea into the next round and handed Brendan Rodgers his first competitive win as manager.
Pascoe told the official site: "Barnet made it very difficult for us early on by pressing us well.
"In fact, if it wasn't for some great saves from Dorus de Vries, we could have been three or four down in the first 20 minutes.
"But with the possession we eventually had, once we scored the first goal we were always on top.
"It was nice to see Joe Allen back after injury and I thought him and Scott Donnelly did well together in midfield.
"Young Joe Walsh also did well on his debut at left-back, while I thought Shefki picked himself up well after missing the penalty to score a fantastic goal at the end.''
This article first appeared on JACKARMY.net.