Howe was speaking to the Daily Echo immediately after Cherries had been given a home tie against League Two outfit Northampton in the second round, with the draw having taken place earlier tonight.
Cherries, who booked their place following a 2-0 win at Exeter last night, will host the Cobblers during week commencing August 25, probably Tuesday, August 26.
Howe admitted a home draw had come as a relief with the tie sandwiched between two away trips for Cherries in the Championship – at Blackburn and Norwich.
Cherries last reached the third round in 2004-05 when Howe was on target in a penalty shootout at Ewood Park to earn them a home tie against Cardiff City.
Howe told the Daily Echo: “We will need to be at our best if we want to progress. A home draw was what we were looking for and we were delighted to get one.
“The draw has given us a tough assignment and Northampton will be full of confidence after knocking out Wolves at Molineux last night.
“Having beaten Championship opposition away from home, they will fancy their chances against us and we will need to be on our mettle.”
Discussing the possibility of a cup run, Howe added: “There are some great stories told in this competition and there are some great games which can be opened up if you manage to progress and why not go on a cup run to supplement our league form.
“When you have a squad the strength we believe we have then a cup run is essential to us to get the players minutes and keep everyone involved.
“Bradford reached the final not so long ago and what an occasion that is. It would be talked about for many years if that were to happen here. I am not saying we are going to do that but we would certainly love the chance to.”
Cherries, beaten by Northampton in the second round in 1964-65, eliminated the Cobblers in 1994-95 before going on to lose to Chelsea over two legs in the second round. The Dorset club’s best run in the competition came in 1961-62 and 1963-64 when they made the fourth round.