The Chairboys stunned Fratton Park by taking the lead in just 13 seconds through Joel Grant's curler. Dean Morgan doubled Wycombe's advantage after nine minutes before Pompey striker Izale McLeod pulled one back in first-half stoppage time.
But Morgan finished the job when he headed home the rebound from his own penalty after 55 minutes, which was brilliantly saved by Pompey goalkeeper Simon Eastwood.
Appleton said: "The three points on Saturday are more important than going through to the next round of this, but that's no excuse. We would have loved to go through to the next round.
"I didn't really want to give the players too much feedback because I'd have probably ended up losing my rag if I did. From my point of view, we need to move on very quickly - a win here would have been 10 times less important than picking up three points on Saturday. We all know that.
"But the one thing we have to improve on is coming out of the blocks quicker. We didn't have enough in the locker to get back in."