The Dons manager Stuart Murdoch saw his young side come from behind to dump Nationwide Division One leaders Pompey out of the cup and then insisted: "We could have had more than just three goals."
Dons defender Mikele Leigertwood scored the first senior goal of his career as the Londoners sentenced in-form Pompey to their first home defeat of the season to book their place in round three.
But it was Pompey who made the better start and they were rewarded when French striker Vincent Pericard headed his fourth goal of the season after Paul Merson had crossed from the right.
Wimbledon winger Jobi McAnuff, a one-time Pompey target, drew the Dons level less than 60 seconds later.
The teenager fired a 25-yard piledriver that deflected off Pompey defender Matt Taylor wrong-footing goalkeeper Shaka Hislop before nestling in the back of the Fratton Park net.
Central defender Leigertwood made it 2-1 after 15 minutes when he headed home the first goal of his career after Alex Tapp had picked him out unmarked at the back post with a pinpoint corner from the right.
Striker Neil Shipperley made it 3-1 13 minutes into the second half to all but secure Wimbledon's place in round three after Taylor had had a goal ruled out for offside.
Top scorer Shipperley rose brilliantly at the back post before heading home the Dons' third after McAnuff had crossed from the right.
Delighted Wimbledon boss Murdoch afterwards paid tribute to his team of teenagers, saying: "We could have secured the win before half time and to be honest we could have had more than three goals.
"But I can't praise my players enough. They are young lads trying to cope under very difficult circumstances and I thought they were absolutely terrific."
Portsmouth manager Redknapp did not share Murdoch's enthusiasm, saying: "Some of our defending was absolutely awful.
"We badly missed Arjan De Zeeuw who was injured but to concede two goals from set-pieces is unforgiveable."