Saints assured themselves of fifth place in Super League on a night when England international James Roby returned from ankle ligament damage to start.
Roby's return was great news for both club and country and his performance - which helped set up an all-but-certain play-off with Hull KR - along with Swift's, pleased Australian Brown.
"I thought we were a bit scratchy in the first half but we scored some really well-constructed tries in the second half," he said.
"Adam Swift is going really well and he's working hard on his game. James Roby came through the game as well, which is a bonus for us."
Former Hull man Willie Manu scored one of Saints' tries - his latest contribution after a tough start to his career at Langtree Park.
"The team is learning how to use Willie Manu better and you can see the difference. The way you use him is important," Brown added.
Leeds won the title from fifth last season and that is now a task which sits ahead of Brown and his men.
"I hope the logic [of ending fifth and winning the league] is right then," he said.
"We are not afraid of going away from home. I think the competition is a lot stronger than it has been in the past.
"The bottom four teams in the play-offs are all really strong teams. Years ago, apart from Leeds, there weren't any teams that were going to threaten the scorer. If teams don't play well, they'll get beat."
Hull FC head coach Peter Gentle felt his side were guilty of gifting their opponents an opportunity to win the game.
"We gave them a massive leg-up. We were our own worst enemy and we lacked composure. We were up against a really good side there and we gifted them 22 points in the first half," said Gentle.
"We will have to address our errors and we will address it. The skill level at times was appalling. To come in at half-time 22 points down was extremely disappointing.
"We started the second half well and had a lot of pressure down their end but then we seemed to panic again."
Hull must now wait on Catalan Dragons' result this weekend to see if they will head to Perpignan or face the French team at home in the play-offs.