A win against Leicester saw the Magpies reach their first League Cup semi-final for 47 years to set up a clash against the Saints, who dumped Manchester City out of the competition.
The Magpies will travel to the south coast for the first leg on Tuesday, where they are aiming to edge closer to their first piece of domestic silverware in nearly 68 years and Howe believes just reaching the final four is not enough.
"We're delighted to be where we are, but the semi-final itself isn't enough, I don't think it's enough for anybody," he told a pre-match press conference.
"I think you go into these games and to say you got to a semi-final is nothing, ultimately, you want to get one step further, I know the players feel the same way.
"Me and my coaching team feel passionately about it that we want to make the final, but we have to navigate these two games, they're going to be very difficult, as I say.
"We want it to be a tie for the supporters, the only way we can guarantee that is performing at our best.
"I think the away game will be a really good spectacle for the fans that travel, it's on telly so everyone will have a chance to watch the game.
"The home game will be a very, very special night, our job is to make sure we're in a good position going into that tie.
"We're desperate for the next step but we have to take our mind off that really and focus on the process and the job, and the job is to go to Southampton and perform."
Newcastle go into the match having extended their Premier League record to 15 games unbeaten with a goalless draw at Crystal Palace over the weekend.
Opponents Southampton are bottom of the table having struggled in the league this year, but they are under new management following the appointment of Nathan Jones in November and have had success in cup competitions this season.
As well as stunning City in the quarter-finals of the Carabao Cup, the Saints reached the fourth round of the FA Cup and Howe was full of praise for his opposite number in the dugout.
He said: "Ralph [Hasenhuttl] had his way of playing, Nathan's got his, there are subtle differences, as I say, not drastic changes.
"Nathan I admire greatly as a manager, I think he's done very well in his career, looking at his time at Luton, what job he did.
"He's now gone to a new club and he's looking to implement his ideas there, we know with a new manager, new players coming in it's a different challenge to one we faced under Ralph.
"I think with the cup game as well it's a chance for both teams to get away from the Premier League and the pressures that brings, that'll be an interesting dynamic going into these two games."