The club is third-bottom of the division after failing to win any of its six games so far this season.
Newcastle held Crystal Palace to a goalless draw on Saturday in front of watching owner Mike Ashley.
Lascelles recovered from an ankle injury in time to play at Selhurst Park, where Rafa Benitez’s side spent much of the game on the back foot.
And United’s captain is now focused on Saturday’s home match against Leicester City.
“We set our goal to win at Palace,” said Lascelles. “It didn’t happen, but we take the positives, of which I think there were a lot, and we go for the three points next weekend because that first win need to happen soon.”
Lascelles is adamant that the players’ confidence has not been dented by their seven-match league and cup winless run. However, the 24-year-old wants the team to be more “positive” going forward.
“Of course the self-belief is high, especially after the draw,” said Lascelles. “We went up against a top, top side who are very good going forward, and we stopped them playing good football.
“Now we just need to build, work on our strengths, and be a bit more positive and go for games attacking-wise in the next few weeks.”
Lascelles had been forced off against Arsenal the previous weekend, having gone over on his ankle in the warm-up at St James’s Park.
“I had an injection in it the other day, and it feels much better now,” said the former England Under-21 international.
Wilfried Zaha, the home side’s in-form forward, had a quiet game.
Palace manager Roy Hodgson felt that Zaha had been distracted by the fallout from his call for more protection from referees.
“I don’t think he expected his comments to be treated as they were,” said Hodgson. “I think it was a justifiable lament.”
United doubled up on Zaha, who was eventually swapped to the right side of Palace’s attack.
“Everybody knows he’s a good player, and, on his day, he’s sometimes unplayable,” said Lascelles. “But I thought DeAndre (Yedlin) did well, and then Dummy (Paul Dummett) did when he went to the other side.
“In the wide areas they’re very dangerous, but we coped well with that threat. That’s something I’m pleased with.
“If their players aren’t doing it in the wide areas, then we’ve done our jobs as defenders. I’m pleased with the boys – individually and collectively.”
Lascelles was pleased with how the team defended, especially during a fraught final few minutes.
“Defensively I’m very pleased with how we’re going,” said Lascelles. “Another clean sheet at Palace, Feddy (Federico Fernandez) was excellent, the goalkeeper was excellent, so were the full-backs.
“Everyone on the pitch was spot-on defensively. It’s about keeping the same intensity and team spirit, because we’re at our very best when we play like that.
“We are pleased with a point.
“I thought we did that excellently, so now we need to keep this momentum and take it into the Leicester game.”
Lascelles says the players didn’t know that Ashley would be attending the game.
“We didn’t know he was coming,” said Lascelles. “We were focused on the game.”