The skipper had issued an apology on behalf of the players after the Magpies' humbling at the King Power Stadium at the end of September, but the visit of the Red Devils seven days later was watched by 51,198 fans - the biggest St. James' Park crowd of the season so far.
Teenage midfielder Matty Longstaff's goal on his Premier League debut sent them home happy and captain Lascelles was delighted to give the United faithful the result they deserved.
"Especially after the Leicester game - they travelled down there to watch us play and we lost 5-0 so we do feel for the fans when things like that happen," Lascelles told nufc.co.uk.
"It's nice to bounce back and get a result for them. The atmosphere was great on Sunday, they were behind us for the whole game, and it makes a big difference when they do that. We're very thankful for that and we're just glad that we gave them three points.
"Things change really fast in football, going from a bad experience down at Leicester, losing 5-0 and having a tough week in training, then in the next game playing Man U; you do fancy yourself, but at the same time you know they're a world class team so it doesn't get any easier.
"But we rolled our sleeves up and we got a big reaction. That's exactly what we needed, so it's been a really good week."
Head coach Steve Bruce shuffled his pack at the weekend, making five changes including first starts of the season for DeAndre Yedlin, who had missed the opening weeks of the campaign after undergoing a groin operation in the summer, and Ciaran Clark, as well as handing 19-year-old Longstaff his bow.
Lascelles said: "The manager made a few changes; we know how hard a job it is for a manager to drop players and put players on the bench, but he's put Matty Longstaff in there, added Ciaran to the team and obviously Allan (Saint-Maximin) was back in the team, so a few new faces who haven't really featured this season and they did a great job.
"It was a fantastic debut for Matty - you couldn't write it - and I was pleased for him and his brother that they were playing together. All over the team, we were enthusiastic, energetic, in their faces. We've set our standard now and that's how we always need to play. Nothing less.
"We'll enjoy this little international break and after that, we'll start planning for another big game at Chelsea. I think momentum is a big thing in football but I think a little break won't do us any harm and we can refresh but still knowing that we've just beaten Man U, and we're still on a high from that, so hopefully we can go into the Chelsea game full of confidence."
