The left-sided midfielder opened the scoring midway through the first half of Sunday's clash at the Kingston Park Stadium, but it wasn't enough to earn three points as Becky Langley's side conceded a late equaliser which saw the game finish 1-1.
Following the match, Elson expressed her belief that the visitors outfought the Lady Magpies and were good value for their point.
"We were not the desired team," she said. "We didn't put in half as much desire as they did.
"They wanted it more. They managed to (take points off us) again and it's not good enough from the girls."
Elson's first-half strike from outside the box was her third of the season, having carried her prolific finishing into 2022/23 following a fruitful pre-season.
But Newcastle's number 11 maintained that getting on the scoresheet means nothing to her if the Lady Magpies don't come away with a positive result.
"(Scoring) doesn't bother me," she declared. "It's not getting us the three points and that's all that really matters.
"We set ourselves goals throughout the season and the only goal we have is promotion. (Our performance was) not good enough."
The draw with Chorley was the second time in consecutive fixtures that a visiting team have taken points away from Kingston Park, following Newcastle's defeat to Hull City Ladies two weeks ago.
But despite a disappointing couple of weeks, Elson reiterated that "there is nothing to worry about", urging her teammates to turn their attention to future fixtures.
"We know what the league's like," she said. "We are going to give everything in every game and that's all we can do.
"We've lost points, but we move on now; we forget about it. We move on and we go for the next three points."
The Lady Magpies will have to wait a couple of weeks before they are in league action again, as Langley's side faces a trip to Lincoln City's LNER Stadium on Saturday.
Elson is optimistic going into this FA Women's National League Cup fixture and believes the experience of playing at St. James' Park and Kingston Park will bode well for the Lady Magpies at the home of Lincoln City.
She said: "The opportunity itself is good that the women are being given that. We've gotten used to a big crowd now, so I don't think it will change how we play.
"We are used to that environment now and I think we need to stop focusing on the environment and focus on what's on the pitch."
She added: "Our aim is to (do well in cup competitions). I think this year we should be pushing on and pushing further to get into them big games."
Photograph courtesy of Colin Lock/@Tyneside_NUWFC