Eunan O'Kane scored in the 53rd minute to put the Cherries into the second round for just the second time in eight years and Howe says a cup run would be very welcome.
"I am delighted to be in the hat for the next round, because these games against lower league clubs are never easy and Portsmouth are a good side," he said.
"We have a dreadful record in this competition so hopefully we can go on a run now. We would relish playing a Premier League side in the next round."
Pompey boss Guy Whittingham said: "I was pleased with the way the team played for the whole 90 minutes.
"This is a tough place to visit and the team gave a decent account of themselves, although we are clearly disappointed to go out in the first round
"We made six changes to the team and it will take a while for the team to gel together. I want to give every player a chance."