Andy Frampton bagged a double for the Dons, having previously scored just twice in the last four years, while a fine 25-yard strike from Sammy Moore and a late Michael Smith effort put the gloss on the win.
The Londoners even missed a penalty when it was still goalless - Harry Pell seeing his effort saved by Pompey goalkeeper Trevor Carson.
Whittingham, who last week celebrated a year in charge, said: "It's a defeat that really makes you think deep about how you put things right.
"We'd been going very well up until last week and within a week we've lost three games.
"You have to think back to going back to basics. We've conceded far too many goals the past two games through basic defensive errors - and I'm not just talking about defenders I'm talking about as a whole team. That has to be put right.
"When emotions are running through everybody you can shout all you want but you have to try and talk sense. It's a result that's very hurtful.
"It's not a case of protecting players, we're all in this together and we weren't good enough. We all have to put that right.
"You go into their changing room and you hear their changing room buoyant and celebrating and we sat and listened to it. I made everybody hear it because it's not a nice thing to hear and it shouldn't be."