The buzzing Bees did not get their second goal until past the hour mark and they led just 3-0 with three minutes of added time left on the clock.
Late goals compiled a miserable afternoon for Saints, who remain rock bottom of the Premier League with just six points from 20 matches.
It is the joint-worst total at this stage of the season in the league’s history and comes despite Ivan Juric’s appointment as boss two weeks ago.
Frank dealt the Croatian his third consecutive defeat in the post and was asked whether he felt Saints had given up trying to stop Brentford by full-time.
The Dane responded: “Maybe. Honestly, I was not focusing too much on that. But of course, I think it’s a fair point. I wanted the 2-0 and the 3-0.
“You never know in football. We wanted to continue going for the next goal, and my players relentlessly went for the next goal and the next goal.
“Of course, we need to back it up with other wins on the road but if we look at the performance, I think it’s one of my biggest moments.
“Biggest moments in terms of performances with this Brentford team in the Premier League, to go down here against Southampton.
“There are no easy games in the Premier League against a team that is fighting to stay in the league. New manager, new energy.
“We’re going away from home which always is more difficult. And then win in the way we did it, where I think we were in complete control and dominance.”
Saturday marked three years since owners Sport Republic purchased the club in January 2022, when they beat Brentford 4-1 at home in their first match.
