Pompey had more possession and more clear-cut chances, but it was Chelsea’s youngsters who left Fratton Park with the victory.
The Checkatrade Trophy third round tie looked to be heading for penalties when Brett Pitman cancelled out Charly Musonda’s opener in stoppage-time.
But there was still time for Musonda to curl home a free-kick at the death to ensure it was the under-21 side who reached the quarter-finals.
Jackett did not believe it was bad luck that cost his men, however, and felt they were simply not clinical enough.
The Blues boss said: “We had the majority of the ball, but didn’t really get enough shots away or test Chelsea enough.
“There were a lot of set-pieces in both halves of the game and they have to be better in terms of delivery.
"We didn’t do well enough in front of goal for all the effort we put in and that has cost us a potential Wembley appearance."
“It’s something that has just been far too inconsistent for us ever since Gareth Evans has been out injured.
“Chelsea are obviously a good technical side, but we didn’t do enough to work their keeper for the amount of the ball and territorial advantage that we had.
“You have to put your chances away, make those runs across the near post and hit the target if you want to win games.
“They scored at the end because of a good break and we probably should have got a tackle in earlier because the boy ran a long way.
“We showed him too much of the goal for the free-kick and it was too easy for him. We offered the chance and he took it.
“Overall, we didn’t do well enough in front of goal for all the effort we put in and that has cost us a potential Wembley appearance.”
Nathan Thompson and Ben Close both limped off against the Londoners, leaving doubts over their availability for the next league game.
Jackett said: “Thompson has an ankle injury, while with Close it seemed to be a severe bout of cramp, so we’ll see with both of them.
“If they’re not fit for Scunthorpe on Saturday then that’s something we’ll have to deal with and we’ll go with what we do have.”