Allardyce's side were outplayed for the majority of the 1-0 defeat at the KC Stadium, but he focused on the performance of the referee rather than his own team.
The Hammers boss claimed Brady used "simulation" to "buy" a penalty, but Bruce defended the Irisman's integrity and insisted he would discipline any of his players should they be seen to dive.
"I'm not going to encourage anyone to cheat and neither is Sam," said Bruce. "Over the years we've built reputations of teams being honest and I'm not going to condone that.
"There was contact, how big or not I don't know. I'm not going to pull the wool over anyone's eyes, certainly if I caught any of my players trying to cheat - and that's what it is, let's not beat around the bush - I would punish them.
"But it looks to me as though there was contact."
Bruce's side now have three wins this term, leaving them well ahead of schedule in the fight to survive in the Barclays Premier League.
Record signing Tom Huddlestone has been a cornerstone of their eye-catching start to the season, gaining plenty of plaudits for the way he dictates play from a deep-lying midfield position.
The former Tottenham man, the Tigers' marquee summer signing, won the man-of-the-match honours against the Hammers and continues to repay Bruce's £5.25million outlay.
"Tom is our record signing and he carries it very well," he said. "He's a wonderful footballer who makes the game look so easy. He's never been a regular in a team for a long time and can only get better.
"He is relishing playing week in, week out, and perhaps being a big fish in a small pond.
"Week in, week out, people are purring at watching him play and I have never seen anyone who can kick it with both feet do it as well as he can. He makes the game look so easy."