Wanderers took a massive step toward survival in the Premier League after Matthew Taylor's late brace at the Britannia Stadium moved them seven points of the bottom three.
Yesterday's result seemed unlikely after a first half the Potters had dominated, Dave Kitson giving them the lead in the 13th minute after latching onto Tuncay's pass and rounding Jussi Jaaskelainen.
But Bolton emerged after the break with all guns blazing and Taylor turned the match around, drawing things level with a free-kick five minutes from time before netting the winner three minutes later.
Coyle labelled Wanderers' first-half performance "unacceptable", but having let his players know it, the manager was pleased to see them make amends in the second period.
"The first half I felt we were as poor as we have been, certainly since I have come here," Coyle said.
"But if you're asking where did the win come from, you just have to watch the second half.
"I thought we should have equalised before we did and there is no doubt in my mind that we were the team in the ascendancy.
"I thought the second-half performance was of a very high standard and if you analyse it, I think we merited the three points - accepting it was very late, but that is the nature of football."
He continued: "My focus (at half-time) was on trying to get back into the game, one I still believed we could win.
"I genuinely believed that and the players will tell you, because they know what I had to say to them.
"There was certainly one or two choice words used, because I felt they were well below what they can offer for this football club.
"The way we were losing in the first half wasn't acceptable for me, but we answered that in the second half and I thought the response was outstanding from each and every one of them."
The win takes Bolton up to 14th and seven points clear of the drop zone with three games to play, but Coyle is in no mood to relax just yet.
"Until we are mathematically safe, it certainly is never enough," Coyle said.
"Hull have a game in hand against Aston Villa and they will try and get points there.
"It is a big, big ask (to survive) because we know every team down there is fighting for their lives.
"What we have to do is go and try and get more points - two of our last three games are at home. It is really in our own hands and the sooner we get those points the better."
Stoke boss Tony Pulis noted that referee Stuart Attwell seemed to pause before awarding the free-kick that led to Bolton's equaliser.
"What surprised me was the hesitation," Pulis said.
"If it's a free-kick, it's a free-kick and he's seen it. Why does he let it run for two or three seconds, then bring it back? But we have to take it on the chin."
Pulis also claimed the officials had got it wrong in the first half when he was adjudged to have handled the ball before it had gone out of play.
He said: "The linesman said the ball hadn't gone out of play and how he can say that is just amazing.
"It was a drop-ball because I apparently encroached on the pitch. The ball was definitely out."
Pulis said he had no problem with Tuncay - who went straight down the tunnel after being substituted in the second half - but stressed he would not hesitate to make the same decision again.
"It makes no difference - if I have to take him off next week, I'll take him off," Pulis said.
"If by doing that he thinks that is going to affect me and what I do, that won't be the case - I will always do what is best for the team."