The Blues thrashed their non-league visitors 6-1 at Fratton Park to move into the third round of the historic competition.
Rasmus Nicolaisen and Tom Naylor put Pompey ahead at half time, before Sean Raggett, Marcus Harness, an Ellis Harrison penalty and Jordy Hiwula’s strike gave Pompey an emphatic success.
King’s Lynn, 12th in the National League are 56 places below Jackett’s side – fourth in League One – in the football pyramid.
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Had they pulled off an upset, it would have arguably been the giant-killing of the second round.
But Jackett praised how his Pompey troops didn’t underestimate their opponents to deliver a comprehensive victory.
He said: ‘We did well. We got off to a great start with Rasmus Nicolaisen's header giving us a chance to get us a great start.
‘We were in front in the first few minutes, which was excellent.
‘It gave us a chance to get through to this particular round and didn't want to slip up because it was a potential banana skin.
‘We worked very hard at Ipswich in the first round to get through and now we are into the third-round draw, which we are pleased with.
‘Despite making five changes, the energy levels were good.
‘We didn't want to be a banana skin. We understand it can be difficult but when we get draws like this, we want to be professional and play well.
‘We looked like we have goals in us, which is a good thing.’