A close-range shot from Jon Walters appeared to go over the line but Foy allowed play to continue and Tottenham secured a 2-1 victory, thanks to a brace from Gareth Bale.
Walters, making his debut after arriving from Ipswich, was first to react after Heurelho Gomes blocked a far-post header from Ryan Shawcross.
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"It was a foul on the goalkeeper, a blatant foul by Robert Huth. He has pushed him with two hands," said Redknapp.
"I saw it on the replay and that is what Gomes told me in the dressing room. I didn't see it when it happened."
Foy's decision puzzled Stoke manager Tony Pulis, who said: "The first one (by Shawcross) looked a foul but if he doesn't give it then it is goal.
"Why he (Foy) has got his head up and looked across at the linesman on the far side when he was only two yards away goodness knows.
"Sometimes they go for you, sometimes they don't. I don't think any referee goes out there to make a bad decision now. You have to take it on the chin."
Bale made the breakthrough in the 20th minute when he headed home after getting on the end of Shawcross's clearance.
Ricardo Fuller pulled Stoke level five minutes later after poor defending by Younes Kaboul. However Bale regained the lead for his side in the 30th minute with a spectacular volley into the top corner.
Redknapp added: "We deserved to win because in the first half they could not get near us. We passed the ball in fantastic fashion."
Source: PA
Source: PA