Brown was thrilled to see the league's bottom side win 2-1 as second-half goals from John Baird and Jim McAlister cancelled out Dougie Imrie's early opener.
Brown said: "I'm delighted for the players after that. They gave me everything and that's all all I can ask for. They never looked like giving in even when we went down 1-0 in the first half and weren't playing all that well, so they deserved to get the win in the end.
"They showed what they're all about and to keep going the way they did speaks volumes for them.
"We need everyone pulling together which is what we got tonight. It's still going to be difficult to stay up but this will at least give us some hope for the rest of the season."
St Mirren manager Danny Lennon admitted his side had only themselves to blame for throwing the points away.
Lennon said: "It was Jekyll-and-Hyde stuff from us. It means getting into the top six now is going to be a very tall order.
"We got off to a dream start but never took it on and I didn't expect what happened to happen. The way we took our foot off the pedal is the most disappointing thing about this defeat.
"I decided to try to freshen things up beforehand by making a few changes so maybe I've got to look at that aspect as well.
"We spoke before the game about how fired up Dundee would be as John Brown is a real motivator. But we let them back into the game when we shouldn't have which is our own fault."