Saints won 1-0 at Wembley thanks to Adam Armstrong's strike.
Southampton boss Russell Martin later said: "I feel really emotional and overwhelmed by the support I have had over the last nine or 10 months, especially in the tough times.
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"For them to give me the job in the first place, I felt like I had to do this to justify and validate it so I'm so pleased for them because it wasn't an exciting appointment for them, I finished 10th at Swansea and had a really clear way of doing things at MK (Dons), and now here.
"So to take me on was really brave. The team have been so great and I'm really grateful and proud of them.
"It's not about me now, it's about them, I really believe that.
"They were trying to drag me up there (to lift the trophy) but they deserve it."