It's a competition the Blues have never won, since their introduction to the League Cup in the 1960-61 season.
In fact, the quarter-finals is the furthest Pompey have progressed in the 58 consecutive years since.
Here,Â we look back on their record in a cup never to grace the boardroom at Fratton Park.
Is that true? Is the quarter-finals the furthest Pompey have ever got in the League Cup?
I'm afraid so '“Â but it's a stage they've reached on five occasions.
The first came in the competition's inaugural season '“1960-61.
That year Freddie Cox's side beat Coventry (2-0), Man City (2-0) and Chelsea (1-0) on their way to the last eight, before being beaten 1-0 by beaten finalists Rotherham 3-0.
The season 1985-86 was the next time the Blues went on a decent run in the competition '“Â then known as The Milk Cup.
Victories over Gillingham (two legs), Stoke and Spurs (after two replays) set up a quarter-final tie against Jim Smith's Oxford.
Yet Alan Ball's side fell victim to a 3-1 defeat against a U's side who went on to beat QPR in the final at Wembley.
Smith, now in charge of Pompey, then proceeded in taking the Blues to the last eight in the 1993-94 season.
However, he was denied another Wembley run-out by Alex Ferguson's Manchester United.
After defeating Rotherham (5-2 over two legs), Swindon (2-0) and Peterborough (1-0 after a replay), the Blues were handed a trip to Old Trafford in the quarter-finals.
Paul Walsh scored twice as the visitors earned a 2-2 draw and a replay back at Fratton Park.
However, it was the Red Devils who progressed to the semi-finals, with a Brian McClair effort separating the two teams.
Watford ended Pompey's run to the last eight in 2004-05 with a 3-0 victory at Vicarage Road, while Avram Grant saw his Blues' route stopped by Aston Villa in 2009-10 (4-2), following earlier-round wins against Hereford, Carlisle and Stoke.
So what's Pompey's recent record like in the League Cup?
It's not great, to be fair.
Their last win in the competition came during the 2015-16 season '“Â a 2-1 victory against Derby at Fratton Park
Adam McGurk and Conor Chaplin goals either side of Jason Shackell's effort saw Paul Cook's side set up a second-round tie away to Premier League Stoke, who ended up beating the Blues 4-0.
Since then, they've beÂ been beaten inÂ the first round by Cardiff and Coventry '“Â both after extra-time.
Prior to the Derby win, the Blues lost first-round ties against Bournemouth (2013-14), Plymouth (2012-13) and Barnet (2011-12).
The 2010-11 season makes for better reading.
Goals from Nadir Ciftci and Michael Brown earned Steve Cotterill's team a 2-1 win at Stevenage.
That was then followed by a 4-3 penalty shootout victory against Crystal Palace, before a 3-1 third-round loss at home to Leicester.
Come on, surely we can excuse that defeat to Plymouth back in 2012-13?
You're right. Looking back at the circumstances back then, defeat was almost inevitable as then- boss Michael Appleton had to field a near-youth team at Home Park.
Pompey,Â who had to release all senior players to avoid liquidation that summer,Â fielded nine teenagers in their starting XI.
And when first-team coach Ashley Westwood, 35,Â went off injured, that left the Blues'Â entire outfield side aged 18 or under.
Seven of Pompey'sÂ team had not played a senior match beforehand, while Appleton could only name three substitutes '“Â including a 15-year-old Jack Whatmaugh.
So how do we finish this read on a positive note?
Well, let's not forget that Pompey go into tonight's match against Wimbledon with a 100-per-cent winning start to the 2018-19 season.
Also, you might not be aware of the Dons' recent record in the League Cup.
Believe it or not, but Neal Ardley's side have yet to progress beyond the first round since their promotion to the Football League for the 2011-12 season.
That makes for seven straight defeats for a side which seems to struggle in this competition.
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