Newcastle United boss Eddie Howe declared themselves a "club on the up" after reaching the Carabao Cup final.
Howe's side led 1-0 after the first leg at St Mary's, and extended their advantage after five minutes through Sean Longstaff's low shot.
Longstaff scored again 16 minutes later following Miguel Almiron's pullback.
Southampton's Che Adams scored from 25 yards but the hosts still won despite Bruno Guimaraes being sent off.
"It was an intense game. At 2-0, we were playing really well and their goals changed the dynamic." said Howe.
"Part of our problem was the psychological aspect. Southampton had nothing to lose and we were feeling the pressure.
"You want to be in finals of competitions to increase your status and make yourself more desirable for people to join. This is a club on the up."
On goalscorer Longstaff, he said: "He is pivotal. He's Newcastle through and through. I think he's an excellent payer and adding goals will only improve other people's awareness of that. He's been great this season.
"I've always believed he's an excellent finisher and converting that to a game is difficult. I always believe if you get in the right areas it will come together and he did that today."
On whether he'd pick winning the EFL Cup or a top four finish, he added: "I can't choose between them. We are going for everything. As much as we can achieve, we will go for."
