Pierre-Emerick Aubameyang's composed finish towards the hour mark secured three points for the Gunners despite Newcastle's promising first half display, which saw Jonjo Shelvey hit the post with a fierce strike and club record signing Joelinton go close on two occasions.
Lascelles was left disappointed after a defensive error led to the only goal of the afternoon and felt the Magpies deserved a positive outcome at St. James' Park after restricting Unai Emery's side to a lack of clear-cut goalscoring opportunities.
The defender told nufc.co.uk: "Overall, there were a lot of positives to take. We can't drop our heads too much as we played some good football against a very good team. It was a shame we conceded in the way that we did.
"It was very annoying that we did that and I think, overall, we were probably the better team. They had a lot of possession but it was mostly in front of us and side to side which was comfortable to deal with.
"There's a lot of frustration. It was not like they had scored from open play, playing one-twos and getting around us or scoring with quality play.
"It was from our own mistakes and, ultimately, it has cost us three points after a very good performance. We shot ourselves in the foot today and we'll be looking to make sure we do not do that again."
Newcastle face newly-promoted Norwich City on Saturday, 17th August for the Magpies' opening away fixture of the 2019/20 campaign at Carrow Road.
After a close encounter with last season's Europa League finalists, Lascelles was able to take plenty of positives from the Premier League clash against an Arsenal side who finished fifth in the top flight last term.
Lascelles added: "I thought it was a very good first half. We've been working extremely hard in pre-season and we've got a philosophy which I think we stuck by today. We made it really hard for Arsenal.
"They have a quality team and they struggled to play forwards and get behind us at times to get shots away at goal. We need to take the positives from the game and not dwell on it too much."
