The Bees took an early lead through Chris Long before Harry Bunn cancelled it out with a well-taken shot.
However, the Everton loanee restored the lead before Alex Pritchard and Jon Toral put the game to bed.
While not as one-sided as their 4-0 win over Blackpool last Tuesday, the display against the Terriers was almost as dominant.
Button said: “I thought the way we applied ourselves and the way we performed made it look more comfortable than it was. We were very professional.”
The result lifts Brentford back into the top six, although Saturday's opponents Ipswich can retake that place with a win at Leeds tonight.
But the goalkeeper is confident the Bees can maintain their push for promotion to the Premier League.
He added: “We can stay in the top six. We'll set our sights high and see where it takes us. It's certainly down to us and in our hands. We're all confident but we won't be carried away.”
Button is rated by manager Mark Warburton as one of the best goalkeepers in the Championship and the statistics say he is the number one goalkeeper in the second tier.
But the humble stopper played down those plaudits, insisting he was only focused on doing his best for Brentford .
He said: “It's great he's got that opinion on me. I hope to repay that faith for the rest of the season.
“The statistics can be perceived in different ways. I'm keeping my head down and doing what I can for the team. I'm fairly pleased with how things have gone.”