Halsey pointed to the spot as Jermain Defoe went down under Darren Purse's sliding challenge after 30 minutes of the fourth round tie at The Hawthorns.
Jermain picked himself up and tucked away the penalty to level Rob Earnshaw's opener and it stayed at 1-1. The replay is at the Lane on Saturday February 12.
"I thought it was as penalty," said Head Coach Martin. "It was difficult from my view but he turned and was then on the ground and I've seen it a couple of times before, Jermain is not a player to go down without a challenge. I'm sure of that.
"We had the same with Ledley King the other day (against Chelsea) when everyone said it was a penalty but I was sure it wasn't. It's not easy.
Bryan Robson had earlier relayed to the media that Darren Purse had told him that he hadn't touched Jermain, a point the press put to Martin.
"I don't want to speculate," he responded. "Against Manchester United I was confident about the goal because I'd seen it on the screen but I've not seen it again yet."
Martin Jol was sure referee Mark Halsey was right to award us a penalty in Saturday's FA Cup draw at West Brom.