Steve Bruce's side - winless at Anfield since 1995 - took an early lead courtesy of Jetro Willems' stunning strike before trailing at half time following Sadio Mane's brace.
Mo Salah's second half strike confirmed United's defeat and Lascelles admitted, despite a strong start from the visitors, a difficult encounter for the Magpies against the European Cup holders.
Lascelles told nufc.co.uk: "We knew it was going to be a tough game. Liverpool are a good side and we started off really well. Unfortunately, we let them back into the game but, overall, we shouldn't let our heads drop as they're a really strong side.
"The game plan was going very well and we started off brightly. We thought if we defend well, we can do well against them but even if it's a lack of concentration for a second, these teams can hurt you.
United face Brighton and Hove Albion at St. James' Park next weekend as the Magpies go in search of their first Premier League victory on home soil this term.
And Lascelles believes positives can be taken from their encounter against the Reds and insisted his side must now switch their full attention to the clash with the Seagulls.
The centre-back added: "It was a great goal from Jetro (Willems) and I thought we came out of the blocks really sharp. It was just a shame that we couldn't hold onto the lead but we'll look back at the videos and how we could have stopped the goals.
"There were a few mistakes in there but sometimes you have to respect the other team as they are Champions League winners.
"There are positives to take from the first half in particular and we need to make sure we don't let our heads drop. We have a big game against Brighton coming up and it's a one we need to be getting three points from so that's what we'll be looking to do."