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.
However according to Spurs boss Redknapp, Gomes was obstructed in the build-up and Foy's decision was correct.
Redknapp said: "It was a foul on the goalkeeper, a blatant foul by Robert Huth. He has pushed him with two hands.
"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 a 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.
"You are going to come under pressure here. That's the way they play. It is going to start coming in the box second half. You have got to deal with it. You are going to get scrambles and everything else. We knew that.
"It is a difficult place to come. They work their socks off. Tony Pulis gets the best out of his players all the time. They never give you an easy game.
"We could have gone in 3-1 up as we should have scored at half-time. But overall we dealt with the pressure."
Redknapp also paid tribute to Wales full-back Bale.
"Gareth has improved out of all recognition, "said the Spurs boss. "That second goal was one of the great goals.
"To put it in the top corner from where he was was an amazing bit of skill. It was great technique, a great goal."
The result puts Tottenham in good heart for the return leg of their Champions League qualifier against Young Boys on Wednesday when they hope to overturn a one-goal deficit.
However, he believes Jermain Defoe is the only one of the five players injured in Switzerland who has a chance of making it for the second leg.
Stoke have now suffered successive defeats after losing to Wolves on the opening day and Pulis added: "The first half we were not in it. We never pushed up enough and never got close enough to them.
"We pushed on in the second half and looked like the only team that was going to score. But it was not to be."