Goals from Adam Lallana, David Connolly and Oscar Gobern kept the Saints one point ahead of third-placed Huddersfield, with Adkins' side now prearing for Monday's game in hand at Plymouth.
Adkins said: "We've got two games to go and we'll make sure everyone stays grounded. We face Plymouth, who also need to win, and we know what we have to do.
"We will be totally prepared and we'll make sure that every area of the players' requirements are catered for ahead of the next two games.
"I was very pleased with this performance because this is never an easy place to come. Brentford kept working hard and the conditions were very difficult, but we took our early chances and that's what counts at this level.
"When I came here, I wanted us to win automatic promotion and nothing has changed in that respect. I've got a set of players here who are all happy to learn and that is why they have achieved what they have achieved so far."
Source: PA
Source: PA