According to on-screen graphics displayed during the draw, the Addicks were handed both a home tie with Cheltenham Town and an away trip to Exeter City.
The draw was streamed live by the EFL on Facebook but, due to an audio problem, viewers were left to rely on on-screen graphics to learn who each team had drawn.
The graphics then erroneously showed Charlton playing in two ties, with the gaffe causing significant confusion among those watching from home.
Shaun Harvey, the EFL chief executive, compounded the error by reading Charlton's name twice when re-capping the draw.
In actual fact, Oxford United were the team drawn to play Cheltenham, while Charlton will only travel to Exeter.
To add to the confusion, a separate graphical error during the re-cap of the draw swapped Forest Green Rovers and Yeovil Town.
Forest Green appeared to be drawn away to Wolverhampton Wanderers, when the newly-promoted League Two club were in fact handed a trip to MK Dons.
Graphics also claimed AFC Wimbledon and Swindon would play each other, despite both being unseeded teams.
In a statement the EFL said: “The EFL would like to apologise for a number of third party technical issues that affected the coverage of this afternoon’s Carabao Cup Round One draw in Bangkok.
“There were inaccuracies – as a result of human error – in the live graphics output that resulted in confusion and incorrect ties being displayed on screen.
“In addition, some users did experience difficulties in accessing the stream on certain external platforms. Both issues are currently under investigation.
“The EFL can confirm that the draw was not compromised in any way and all Clubs have received confirmation of the Round One ties.”
The draw was held in Bangkok to promote a new commercial partnership with Thai energy drink company Carabao, the competition's new title sponsors.
This was not the first time that one of the competition's rounds has been drawn abroad. Donald Trump, now President of the United States, famously drew the 1991 fifth round from Trump Tower in New York City.
EFL Carabao Cup round one draw
South Section: Birmingham v Crawley, Exeter v Charlton, QPR v Northampton, Southend v Newport, Bristol City v Plymouth, Cardiff v Portsmouth, Millwall v Stevenage, Oxford v Cheltenham, AFC Wimbledon v Brentford, Norwich v Swindon, Bristol Rovers v Cambridge, Peterborough v Barnet, Wycombe v Fulham, Colchester v Aston Villa, Wolves v Yeovil, Reading v Gillingham, Forest Green v MK Dons, Luton v Ipswich
North Section: Coventry v Blackburn, Nottm Forest v Shrewsbury, Bradford v Doncaster, Mansfield v Rochdale, Grimsby v Derby, Barnsley v Morecambe, Crewe v Bolton, Oldham v Burton, Wigan v Blackpool, Bury v Sunderland, Sheff Wed v Chesterfield, Accrington Stanley v Preston, Fleetwood v Carlisle, Sheff Utd v Walsall, Scunthorpe v Notts County, Rotherham v Lincoln, Leeds v Port Vale
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