Although the outspoken boss said it was wrong for players to dive, his comments are likely to spark debate with the issue of simulation once again making headlines in the Premier League.
Allardyce's side were on the wrong end of two penalty decisions in Sunday's 2-1 defeat by Arsenal.
West Ham defender Winston Reid was penalised for bringing down Santi Cazorla in the area, but Morgan Amalfitano later decided to stay on his feet when challenged by Kieran Gibbs and the hosts were denied a late spot kick.
Allardyce said if going to ground is the only way to win a penalty, then players are justified in looking to bring fouls to the attention of officials.
"As long as it's not simulation and you get the right decision from it then it’s fine," Allardyce told reporters ahead of Thursday's home clash against West Bromwich Albion.
"If you're not touched and you go down because you're not touched, that's not the way forward. But if you can't get what you ordinarily should get, then you've got to consider the fact that if you make a meal of it, you make a meal of it because the contact is sufficient enough...
"Referees are not brave enough to give those penalties because, in the atmosphere in the stadiums, it doesn't look like one. But their job is to identify if it is one or not."
Diving is once again a hot topic after three Chelsea players, Cesc Fabregas, Diego Costa and Willian, were booked for simulation this month. Arsenal manager Arsene Wenger called on the FA to ban players retrospectively for simulation.
(Reporting by Toby Davis; editing by Ed Osmond)
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