The Blues delivered a 2-1 victory over the Iron last night to move into the semi-finals of the competition they're currently holders of.
John Marquis opened the scoring in the 13th minute at Fratton Park, but that was cancelled out by Abo Eisa’s 62nd-minute equaliser.
But it was former Scunny loanee Cameron McGeehan who struck moments later with his first goal for Pompey, which moved them to within one victory of a Wembley return.
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Hurst was proud of how his troops performed against opposition from the division above.
Ultimately, though, the Scunthorpe boss felt Pompey were more ruthless in the final third.
Hurst told his club's website: ‘It was a performance against a very good Portsmouth team where we were brave, got on the ball and had a lot of possession. It’s the final bits that matter, and they had two shots on goal in the second half – Rory Watson saved one from Marquis, which would have made it 3-1, but for the one from McGeehan, which was the winner, they were clinical.‘The message before the game was to build on the performance from Saturday (at Bradford) and try to get to those levels again. We dominated large parts of the game for the second match running.
‘We put the crowd on edge and there were a few moans and groans (from their fans) because we dominated large parts of the game.
‘It’s the end of the competition for us so we’re disappointed, but I’ve seen some real positives from the last two games of how we’ve controlled matches and looked a decent team.‘We went into half-time feeling we were well in the game and asked the players to up it because I didn’t feel we went for it as much as we could in the first half.
‘Fair play to them, because in the second period we did do that and got level.
‘At that point, you perhaps thought the team that would go on to win it would be ourselves but they broke and showed their quality with a clinical finish from a player I know the Scunthorpe fans know well, and in the end that was the difference.’
Hurst was disappointed the Iron won’t have the chance of reaching Wembley, but still took the positives from his side’s display.
He added: ‘We’d have been 90 minutes away from Wembley had we won and that’s a frustration because I feel it was there for us, but we didn’t quite do enough to win the game.
‘We more than held our own against a very good team and have to use that as a positive.’