Liam Feeney's strike just before the half-hour mark proved to be the difference between the two sides at the New Den.
But for Jackett it was a case of job done after a solid if unspectacular display against a Preston side who more than matched Jackett's side for large parts of this third-round encounter.
"In the first half we played very well, and created some great chances at the start of the second half," he said.
"We needed to get more goals up really to make it comfortable. We were quite dominant in the first half and had to defend for the last half an hour which was frustrating.
"We had to put in a real defensive shift which we had to sustain for a long period, when they switched to a 4-3-3 formation.
"I'm very pleased defensively that we saw it out. Our passing out of defence before the break wasn't as good as it should have been.
"We hope to get a big draw in the next round for many reasons, and the prize money will certainly help. But it's not a direct translation to money I have to spend on the pitch."