The match marked Lascelles' 150th appearance for the Magpies.
"Every single year in cup games, there are always upsets when lower teams cause problems for the bigger teams," the club captain told nufc.co.uk. "They caused a bit of an upset at their place last time out (a 1-1 draw at Spotland) which wasn't good enough from us.
"We've come here tonight, professional, and took it really seriously. We want to have a run in the cup this year. The next game is against Oxford so there's no reason why we can't have a little run. We just needed to get the job done today, which we did.
"The longer the game went on without us scoring, it probably would have been tougher. We said to ourselves let's keep on top of them and we had a high line and really kept them in their own half.
"Our quality shone through, we stuck to our game plan and then after that, it was about controlling the game and being a good Premier League team.
"The manager has emphasised that we need to take the cup seriously and try to go for a run. He has put a decent side out tonight which he thought could beat them and he's got it spot on. We're happy to get the win.
"All we can do is focus on every game and our next main focus is on Saturday against Chelsea, which will be a tough game."