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.
9. Oxford vs Portsmouth
Ryan Williams and Ellis Harrison rush to congratulate team-mate Marcuss Harness after he opened the scoring. Photo: Robin Jones
10. Oxford vs Portsmouth
Marcus Harness goes in for a tackle during the first half Photo: Michael Steele
11. Oxford vs Portsmouth
Ryan Williams is challenged by Josh Ruffels of Oxford United Photo: Michael Steele
12. Oxford vs Portsmouth
Ellis Harrison holds off Alex Gorrin of Oxford United. Photo: Michael Steele