The former Fulham coach's position had reportedly been insecure after their 6-1 demolition by Serbia (their fifth straight defeat) and if he could not halt that run, there was speculation he could face the sack.
However, a late victory courtesy of Gareth Bale avoided any such talk, with a penalty and an amazing individual strike from the Spurs winger completing a dramatic late turnaround for the Dragons.
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"The pressure really has been ridiculous when you look at what the manager has had to come in to," Gunter told the Daily Telegraph.
"People saying it was a must-win for him to keep his job is a disgrace really.
"I can speak for the players, you only have to see the effort put in against Scotland to see that such talk is just completely wrong. It’s just wrong.
"It's not nice to see. He deserves as much praise as anyone for the preparation ahead of the Scotland game.
"We let a lot of people down in Serbia, including Chris, but hopefully now it is the start of turning the corner.
"We are just delighted to win, you could just see that by the scenes at the end of the game. The way everyone was together.
"We always said the Scotland game was a massive one for us. All week people had been saying it's a must-win. It was a lot of pressure, but I thought we dealt with it unbelievably well.
"I think we showed a lot of character because we have not had it easy over the last few months. So to come out and play as we did against Scotland, particularly in the second half, deserves a lot of credit, both for the manager and the players."
Coleman's men were trailing to Craig Levein's side for the majority of the game through a James Morrison goal, but a late showing from Bale was enough to see Wales put their first points on the board of Group A.
"It's a great feeling to win any game, but to do it in that way was unbelievable," added the 23-year-old Reading full-back.
"It takes character. People were probably thinking it was the same old story when we went 1-0 down.
"To be honest we thought our luck was deserting us again. But we carried on playing our football and doing what we believe in. It paid dividends for us.
"At half-time we said if we kept playing the way we were we would score the next goal, and we would go on and win it.
"We were the better team and that's the way it turned out. Gareth was causing them problems all night. He does that kind of thing all the time. To score a goal like that [second one] is just unbelievable. He deserves all the credit he is getting."