Jeff Hendrick praised the spirit shown by the Republic of Ireland as they claimed second spot in Group D with a smash-and-grab raid against Wales, while goal scorer James McClean hailed an "unbelievable" moment in Cardiff.
McClean scored the only goal of the game in the 57th minute as Martin O'Neill's men became the first side to win on Welsh soil in four years, bagging themselves a World Cup playoff place in the process.
Burnley midfielder Hendrick told Sky Sports: "It was hard work, we knew it would be, but we always said that once we had one game it's a do-or-die and when it comes to the big games this group of lads show up.
"I think everybody that plays us knows they are in for a hard game. We might not pass the ball as much as other countries but we've got the spirit and it's great to do it for the fans.
"We've got two big games, we've just got to keep going and we've got to show that spirit again."
Goalscorer McClean added : "Unbelievable. There's no better feeling.
"A lot of people wrote us off and I think it was a test tonight, even more so because we needed to win, but we showed our character and our quality as well, we dug deep and we'll enjoy this one.
"I remember the ball coming across and it was a great dummy from Harry and as it was coming I was just thinking 'keep it down' and it hit the back of the net. There's no better feeling on a football pitch.
"Look, we're not there yet. it's a big night tonight and we'll enjoy that but it means nothing if we don't go and qualify now."
So you're saying there's a chance 🇮🇪 pic.twitter.com/A0oklIWcAm
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O'Neill paid tribute to his players and a fine finish from McClean.
"The performance of the players was fantastic," the manager said. "We had to withstand a lot of pressure. But we've come through.
"James scored a great goal. Every single time they got into the penalty area, we had men there. We're looking forward to the playoffs."
Ireland withstood heavy pressure from Wales, who again missed out on the World Cup, before McClean scored in the 57th minute, driving home after great work by Jeff Hendrick and a dummy from Harry Arter.
"We could all have realised that that was how it was going to be," O'Neill said. "We said we would have to do without the ball. Once we started getting a foothold, the players got a bit more confidence, and we took it on.
"I've never doubted the character of the players. That's instilled in them. They have great courage. Their courage is never in doubt. Sometimes we can do better with the ball.
"Trying to qualify for the World Cup is a monumental task. But I knew we'd fight back."
O'Neill's team are set for November's playoffs but will be unseeded in Tuesday's draw, meaning they could be drawn against the likes of Italy or Croatia, and possibly Portugal if Cristiano Ronaldo and company can't beat Switzerland on Tuesday.
"I don't think everybody would want to play us," he said. "Do we fear teams in it? Absolutely. Every single one of them. Then we go out and beat them.
"I don't think anyone would want to beat Italy. I don't think anyone would want to face Portugal. And there's six others I would rather not have.
"We have got a lot of work to do. To win in Wales was fantastic. We may lack some things, but courage is not one of them."
ESPN FC's John Brewin contributed to this report.