Carlisle manager Greg Abbott said it was "wonderful" to win the Johnstone's Paint Trophy, a year after being thrashed in the final.
"Last year rocked me massively, I even questioned if I should be a manager," said Abbott.
"To have 14,000 Carlisle fans on your side, and to send them home happy is a wonderful feeling."
Abbott added: "There's not many managers that have been to a cup final and seen their team perform as poorly as my team did last year.
"I stood in front of over 70,000 people knowing I was going to take a lot of criticism and that was difficult, I'm not indestructible.
"Maybe now the fans won't remember last year so much, but instead remember this year. When I have gone and the players have moved on, they'll remember a Carlisle team that won a trophy."
The Carlisle boss also paid tribute to Murphy, who last year conceded the penalty that led to Southampton's opening goal.
"A year is a long time to dwell on something like that. Peter took a lot of criticism last year, but his partner had a baby two days ago and he's scoring the winning goal in a cup final," he said.
"I'm so pleased for him. My decision to play him and keep him in the team was the right thing to do.
"He's been offered a new deal, but we've not talked about it that much. I know he wants to stay but we've got to make sure it's right."