A first-half goal from Dipo Akinyemi saw the Clarets beaten 1-0 by Welling United at Park View Road.
In a tight first half, City found some early joy down the right-hand side, getting in on several occasions.
The most dangerous of the opportunities saw Tom Blackwell send a free-kick to that right flank from deep, where Adebola Oluwo was ghosting in, but his shot was into Coniah Boyce-Clark’s palms.
City’s next chance saw Blackwell again involved, as he got in down the right but no one was able to get on the end of his cutback.
Midway through the half Welling had their first real chance as Alfie Matthews picked up possession with room inside the box but Eduino Vaz ate up the free space and made an impressive block.
Unfortunately for Robbie Simpson’s side, the Wings’ next effort resulted in a goal with Matthews again involved.
The right-sided attacker drilled a pass across the face of goal and it appeared to miss everyone before Dipo Akinyemi was in position at the back post to finish.
Despite Blackwell almost forcing himself a good chance to equalise on his left before his shot was blocked away with five minutes to go, City were unable to find an equaliser before the half-time whistle.
Following the break, the Clarets began the second half brightly but found clear-cut chances hard to come by.
With 15 minutes of the game left, City were just a whisker away from a leveller as Oluwo prodded a shot from a corner at the top corner, but Boyce-Clark made a stretching save to deny him.
The next near-miss for the Clarets came in the final 10 minutes, with a dangerous attack ending in Blackwell seeing a shot deflected narrowly wide.
Despite all of City’s endeavour over the final stages of the game, the home side was able to see out the clean sheet and the game ended in defeat.
In the defeat at Park View Road, Adebola Oluwo’s early effort proved to be the major moment.
While the chance from Tom Blackwell’s ball in from deep was not an easy one, had City taken the lead from the defender’s volley, the afternoon could have transpired differently.
Ultimately, the hosts went on to take the lead with 10 minutes of an even first half remaining before seeing out the points in the second 45.
The Clarets are back in action next Saturday as we welcome Hungerford Town to the EMG Inspire Stadium.
With the Vanarama National League South tie being played on Non-League Day, we are hosting a family fun day with reduced entry prices.
You can find out more on the day here and the kick-off will be at 3pm.
Welling United: Boyce-Clark; Ezinnolm, White, Curran, Statham; Sablier, Margetson, Stevenson (Muscatt 69’); Akinyemi, Derry, Matthews (Pearce 86’).
Unused substitutes: Allen, Burnett, Wells.
Chelmsford City: Dillon; Vaz (Rush 79’), Bradshaw, Oluwo, James; Frimpong (Moore 60’); Dunne (Imray 60’), Isaac; Dada; Sheringham, Blackwell.
Unused substitutes: Dickens, Deslandes.