The visitors' frustrations were then compounded as Williams' delightful strike decided a match that had meandered up until that point, with threats to either goal very sparse.
But the result will come as a relief to the injury-hit hosts, who had lost five out of their previous six games in all competitions.
Robinson said: "I didn't think it was a free-kick for our goal, to be honest.
"If I was in Walsall's shoes, I would have been very, very disappointed in that being awarded - I'm not going to deny that.
"But Shaun has a wand of a left foot, which we have seen consistently in the past with the passes that he makes and he'd had a sighter from a bit closer earlier on.
"He went for the same strike from about 10 yards further out and he's just a wonderful player and a real asset to us.
"I thought we were the better team in the first half although we looked nervous at times and they've only had one chance where Dave (Martin) has made a great save.
"In the second half we huffed and we puffed, but so did Walsall and they didn't really have a chance second half either."
Walsall created the game's first real chance after 18 minutes when Martin made a good save to deny Sam Bantom before Bamford headed over Lee Hodson's deep cross.
After sending an earlier attempt wide, Williams won the points for his side after 64 minutes when his free-kick sailed into the bottom corner.