Late goals form the Ameobi brothers, Shola and Sammy, won it for the Magpies, but it wasn't easy for Pardew's team.
He told Sky Sports: "This was a tough, tough game, make no mistake. We were really under the cosh with the power of that team.
"They're a very physical side, a big, big side, and they had a couple of good chances.
"They really accredited themselves well, the stadium, the fans, and especially the team.
"The second half I could sense we were going to get a goal. It was important for us to get a goal because obviously we haven't scored this year, so to get two goals was a nice bonus."
Pardew felt the introduction of Shola Ameobi and Hatem Ben Arfa changed the game, adding: "We probably wouldn't have won it without that little bit of quality from Hatem (Ben Arfa) in particular.
"And then Shola came on and gave us a bit more power."
Looking ahead to a home tie against Leeds in the third round, as well as Saturday's home match to Fulham, Pardew said: "Well, I'm pleased because it's the first time we've drawn them in the cup.
"We're set for the weekend, we have got no injuries, and that's what you want from this competition - get through and have no injuries."
Meanwhile, Morecambe manager Jim Bentley was pleased with his team's efforts, but was left to wonder what might have been.
He said: "At the end of the day, we have given a great account of ourselves. I think we were the better side in the first half, we just needed to score when we were on top.
"It could have been a whole different ball game. Their crowd might have got on top of them a little bit, it would have given us that little bit more confidence.
"But we gave a good account of ourselves, we had a right good go and I am proud of all the players tonight for their efforts."