James McClean's 57th-minute strike sank Wales and sent Ireland into the World Cup play-offs but Brady faced a nervy couple of days' wait to discover if he'd be retrospectively punished for a tangle with Williams.
The Dragons failed to qualify for the 2018 World Cup, even missing out on a playoff spot courtesy of a 1-0 home defeat against Republic of Ireland on Monday night.
Pulis said: "I just ignored him walking down the corridor".
Pulis himself could be in the running for the Wales job should Chris Coleman decide to step away from the post.
An emotional Gareth Bale was among a group of players who pleaded with Chris Coleman to stay as Wales manager after the team's failure to reach next year's World Cup Finals in Russian Federation. It was a great goal and great technique on his right foot.
"To be fair, I'm pleased for him because he's done brilliantly for me. I look at the Euros and the result against Italy sticks out, and you take confidence from performances like that", the Bournemouth midfielder was quoted as saying by Sky Sports.
"James has most probably done better for Ireland than he has for us but that sometimes happens".
"James is a smashing lad, great around the place".
"I think we paid £500,000 for him and I don't think anyone would say James has been anything but brilliant". "Everyone has respect for him", he said. People don't know James McClean just like people don't know Tony Pulis.
The thing about Tony Pulis banter is that he might not be joking.
Meanwhile, Nacer Chadli has flown to Germany to have his back treated by controversial doctor Hans-Wilhelm Muller Wohlfahrt. "The doc is happy for him to have the injection", Pulis added.