Button was shown the red card after 25 minutes as he raced to the edge of the penalty area and brought down Bradford's leading scorer Nahki Wells with a reckless challenge. The referee took his decision after consulting assistant Bob Roberts, who was in line with the incident.
Rosler said: "David Button decided to challenge Nahki Wells for the ball and, from what I have seen in real time and on DVD, it was a very harsh decision. Our keeper played the ball - in fact, the ball changed direction.
"I haven't decided whether to appeal or not. I will let the emotion settle down and have a good look at it from all sorts of angles and decide what to do. The decision changed the game.
"We should have been in the lead before the sending off and everything looked well, but three of their four goals were presents from us and the second goal was Christmas, New Year's Eve and birthday rolled into one."
Bradford manager Phil Parkinson agreed with the sending off, though, adding: "I thought it was a bad tackle - one of those tackles that can hurt someone."
The Bantams went in front after 40 minutes through striker James Hanson. Kyel Reid played the ball down the left to James Meredith and the full-back cut the ball back into the middle where Hanson scored with a 12-yard shot.
Wells added the second on the hour mark following a long clearance from keeper Jon McLaughlin. Defender Tony Craig tried to head the ball back to Jack Bonham, on for Button, but sent it over the head of the substitute keeper and Bermudian international Wells followed up to tap the ball into the empty net.
Garry Thompson scored the third after 64 minutes with a powerful header from Reid's left-wing cross and Hanson added the fourth with a header at the far post, Reid once again the provider.
Parkinson, delighted with his newly promoted team's start to the season - this win took them up to fifth in the table - said: "There was a really good start to the game. Brentford are the best team I have seen in the division, I thought it would be a really difficult game and we knew we had to be strong defensively.
"Playing against 10 men is not always easy. You have got to be patient and use the ball well and some of our passing in the second half was super.
"I couldn't have asked for more, but we have got to keep our feet firmly on the ground because we know that if we take our eye off the ball we will be knocked back."