Curtis Main netted the only goal in a lethargic contest at The Valley that was watched by very few spectators.
The result ensured that the Blues finished top of Southern Group A and will be at home in the last 32.
Kenny Jackett made eight changes from the side that exited the FA Cup against Luton at the weekend.
Luke McGee, Nathan Thompson and Oliver Hawkins were the only players to keep their place, with the latter two moved to centre-back roles.
Gareth Evans skippered the side at right-back, while Dion Donohue completed the defensive line on the opposite flank.
Danny Rose and Adam May anchored the midfield, with Kal Naismith, Conor Chaplin and Milan Lalkovic making up an attacking trio behind lone frontman Main.
There was also a change made to the substitutes just ahead of kick-off, as Brett Pitman felt a twinge in his knee and was replaced by Christian Oxlade-Chamberlain.
But it was the hosts who got off to the faster start and Anfernee Dijksteel’s cross was turned into the side netting by Karlan Ahearne-Grant at the far post.
Ahmed Kashi then fired a shot straight at McGee, as the Blues felt their way cautiously into the contest.
The Addicks were forced into an early change, however, when Tariqe Fosu hobbled off and Ben Reeves was brought on.
McGee had to come tearing out of box moments later to beat striker Joe Dodoo to a long punt up the pitch.
But Pompey soon found their feet and Naismith picked Hawkins out from a free-kick, with the stand-in defender unable to beat Dillon Phillips from an acute angle.
And they broke the deadlock on 19 minutes, when Lalkovic’s delivery was turned back across goal by Naismith for MAIN to slide home.
He might have had another before the interval, but could not quite make a clean connection to turn Chaplin’s flick on target.
Dodoo was a dangerous presence up front for the hosts, meanwhile, although one shot was comfortable for McGee, while Rose nipped in to prevent him from testing the keeper again.
Charlton’s best chance to level came from one of the opposition players, as Patrick Bauer’s header hit May and was arrowing towards the net until McGee intervened.
Charlton Athletic 0
There was a slow start to the second half, with little to warm the hearts of the small number of fans who had braved the wet weather.
Dijksteel did create an opportunity when he stole the ball from Naismith and fed Billy Clarke, whose shot did little to trouble McGee.
Jackett made a double switch just before the hour mark, with Main and Lalkovic making way for Jamal Lowe and Matty Kennedy.
Pompey soon created a couple of openings, with Hawkins having a header deflected behind after meeting Naismith’s free-kick.
Chaplin then saw an effort blocked and when Lowe picked up the loose ball, he was unable to beat Phillips with a shot.
But, in truth, it was pretty turgid stuff, as both sides went about their business without really looking like scoring.
Lowe was showing a bit more urgency, though, and he surged into the box on 75 minutes before watching his fierce drive parried clear by Phillips.
The introduction of former Blues winger Ricky Holmes also saw the hosts pick up the pace as they went in search of a leveller.
But there was to be no late London drama, as Naby Sarr wasted a late chance to level and the visitors saw out the closing stages to secure their progress.
Charlton (4-2-3-1): Phillips; Dijksteel, Bauer (c), Sarr, Mascoll; Kashi, Aribo; Fosu (Reeves 9), Clarke, Ahearne-Grant (Holmes 70); Dodoo (Hackett-Fairchild 59)
Subs not used: Maynard-Brewer, Barnes, Marshall, Forster-Caskey
Pompey (4-2-3-1): McGee; Evans (c), Hawkins, Thompson, Donohue; May, Rose; Lalkovic (Kennedy 58), Chaplin (O’Keefe 86), Naismith; Main (Lowe 58)
Goals: Main 19
Subs not used: Bass, Burgess, Haunstrup, Oxlade-Chamberlain
Referee: Nicholas Kinseley
Attendance: 1,307 (206 Pompey fans)