The Magpies were frustrated for long periods of the contest but late goals from Shola Ameobi and his younger brother Sammy helped the Premier League club avoid an upset.
"For us that was a big win," Pardew told Sky Sports News. "This was a tough, tough game. We were really under the cosh, but we withstood that then a little bit of quality came through.
"They are a physical side, a big side. But in the second half we got a grip and it was important for us to score, because we hadn't yet scored this season.
"We wouldn't have won it without that little bit of quality."
Newcastle will host Leeds United in the next round of the competition.