The Championship outfit triumphed 1-0 thanks to debutant Marcus Edwards' second-half goal.
Parker said afterwards: "Very pleased. I made a lot of changes. We were clear Southampton would put out their strongest 11 but we executed our game plan and we were well worthy of the win.
"I'm pleased for Marcus (Edwards). He has not had a lot of football and we need to be careful around that. He scores the winner, he has been brought to give us those better habits in and around the box. It's a good start.
"We go into every game trying to win. I'm always very grateful for out travelling supporters and it's always pleasing when we can reward our fans."
On his side's defensive record, Parker added: "(It takes) a lot of hard work. A mindset and mentality in this group, who understand their roles. This was another level up today against a Premier League side, with players who have not played a lot of football. This is a whole unit, a whole team, what we do defensively gives a good platform to win.
"Our main focus now is on Wednesday (against Hull City in the Championship). We need to recover. We will have half an eye on the (FA Cup) draw of course, and we'll see who comes out the hat."