Liverpool looked to be heading for all three points courtesy of Mohamed Salah's superb first-half strike, but Everton snatched a share of the spoils 13 minutes from time when Wayne Rooney lashed home from the spot after Dominic Calvert-Lewin went down under pressure from Dejan Lovren.
Reds boss Jurgen Klopp was livid with the decision, but perhaps unsurprisingly his opposite number was in no doubt the right call was made.
"Don't put your hands on a forward who's in the box, don't touch him, don't push him," said Allardyce.
"If you do, you run the risk of giving a penalty away. He had no need to do it – he could have stood up and shepherded him away from goal, which is where he was going.
"He didn't. He put his hands on him and pushed him over. People can call it soft, but you don't do those sort of things.
"Credit to Craig Pawson for being brave enough to give it at Anfield."