Tomkins was widely criticised for his reaction to a push in the chest from Everton's Kevin Mirallas on Saturday, as the West Ham defender went to ground clutching his face in an attempt to get the opposition forward sent off.
In the 60th minute at Goodison Park, Tomkins initiated contact with Mirallas, pushing his opponent before the Belgian responded, which prompted the 25-year-old centre-back to fall to the ground in mock agony.
Both players received yellow cards and Allardyce was unimpressed on Thursday.
"It was rather silly what James did," he said.
"He understands that. He knows what he did was not right and ultimately he shouldn't be getting involved in the first place.
"It was not the type of reaction you want to see from your players."
Allardyce added: "It's about maturity, isn't it?
"It's about learning from your mistakes. We all make mistakes and those who become better people and better players are the ones that don't make those mistakes again and learn from it.
"So it's a big challenge to James now, whether he has learned from it and whether he is maturing now as an adult."
