The first match finished all square at Fratton Park on Friday night.
Pompey took the lead in the 37 minutes with a strike from Marcus Harness before Oxford United equalised during injury time at the end of the first half.
The teams were unable to be separated after 90 minutes and Extra Time.
Pompey fell to defeat in the penalty shoot out losing 5-4.
See all the best photos from the first half action.
5. Oxford vs Portsmouth
Mark Sykes of Oxford United and Pompey's Steve Seddon in action. Photo: Robin Jones
6. Oxford vs Portsmouth
Marcuss Harness skips past Alex Gorrin of Oxford United during the first half Photo: Robin Jones
7. Oxford vs Portsmouth
Portsmouth fans watching the game from a car park Photo: Michael Steele
8. Oxford vs Portsmouth
Marcuss Harness scores a goal to make it 1-0 (2-1 on aggregate) in the first half. Photo: Robin Jones