In the wake of a 22-10 triumph, Wales coach Gatland could not conceal his sense of pride in a squad that has taken New Zealand by storm over the past month.
They went within a point of matching reigning world champions South Africa, but then reeled off successive victories over Samoa, Namibia, Fiji and now Ireland, scoring 25 tries in the process.
Wales never trailed in a gripping last-eight encounter, and although Ireland recovered from an interval deficit to tie the game at 10-10, tries from scrum-half Mike Phillips and centre Jonathan Davies set up a semi-final against France next Saturday.
The last time the countries met, in Paris almost seven months ago, France won 28-9, but there has never been a World Cup contest between them.
"The boys knew that we were either going home on Monday or we were here until the end of the tournament," Gatland said.
"I spoke to the boys before the game and said they had been fantastic ambassadors. They have worked so hard on and off the pitch, but we were not ready to go home yet.
"We know we are in good shape physically. We've felt we have got better and better as this competition has gone on.
"I don't want to sound arrogant at all, but we were very confident before the game that we were capable of winning reasonably comfortably.
"I do not think any team has worked as hard as we have in the last four or five months.
"Those guys went through some pain (during the World Cup build-up), and when you do that it brings guys together and it galvanises a team.
"I feel that the balance in the team is the best we have ever had."
Once again, Wales' exciting crop of young players delivered when it mattered, and Gatland added: "There is no fear factor.
"We are in New Zealand and not in the bubble of Wales and listening to the pundits every day or any negativity that sometimes comes out of Wales.
"The guys just get on with it.
"We were in a very tough pool, and to come out of it probably helped put us in very good stead for a quarter-final and hopefully a semi-final."
Key to Wales' victory was a colossal defensive effort, especially during the first half when they repelled several Irish attacks close to their line.
Part of the defensive strategy was to tackle low down the leg on Irish attackers, and it worked spectacularly.
"We were under a lot of pressure at times in the first half, particularly in our 22, and I thought our defence was absolutely outstanding," Gatland added.
Wales defence coach Shaun Edwards said: "We kept our structure for a vast majority of the game. I thought our leg tackling was of the highest order.
"It's something we have put a lot of work into, trying to reinvent leg tackling. To do that you need the players who have the courage and technique, and I thought we definitely had that."
Gatland anticipates no problem keeping his squad's feet on the ground as they prepare for Wales' biggest game in World Cup history.
"I don't think it's going to be hard at all," he said.
"We have had a few occasions (post-match) where we have just stayed in the hotel and a couple of occasions when the boys have been able to go out for an hour or so.
"I think they have been brilliant ambassadors. We will go back to the hotel, we will have a recovery day tomorrow and then start planning for the semi-final."
Gatland, though, will be keen for an early fitness bulletin on towering lock Luke Charteris who was forced off at half-time after taking a blow to his shoulder.
"The physios tested Luke at half-time and there was a lot of pain in his arm and not a lot of strength, and we had to make that call," Gatland said.
"I thought Luke's work-rate in the first half and tackle count was absolutely phenomenal, but having someone like Bradley (Davies) to come on and replace him was great for us.
"It will be 24 hours just to assess him, and hopefully it's not too serious. He'd lost a bit of power in his arm, and we had to make that change."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.