Allardyce's Hammers were outplayed for the majority of their 1-0 defeat at the KC Stadium, but he focused on the spot-kick rather than the performance.
He diagnosed a case of play-acting after Brady won a 12th-minute verdict during a slight coming together with Joey O'Brien.
The Irishman was quickly up to convert the penalty, which was enough to secure three points, leaving Allardyce cursing both his fortune and Brady's tumble.
But Bruce defended the midfielder'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. Over the years we've built reputations of teams being honest and I'm not going to condone that," he said.
"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.
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