World Cup - Gatland: We are not finished yet
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 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."
He added: "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."
Meanwhile, Ireland's decision to run the ball and kick for the corners in the opening 20 minutes of their rugby World Cup quarter-final were the right tactics, coach Declan Kidney said.
Ireland chose not to take eminently kickable penalties in the opening quarter after they had conceded an early try to Shane Williams.
Instead, flyhalf Ronan O'Gara kicked for the corner in an attempt to set up try-scoring opportunities from attacking lineouts, despite having the advantage of a strong southerly wind at their backs in the first half.
"I think once they got that early try we went after that try ourselves," Kidney said. "We were in good flow and in good feeling out on the pitch and I think we made the right decisions."
The tactics were backed by captain Brian O'Driscoll, who said the swirling wind had been a factor in his decision.
"We just felt we could keep the pressure on and back the boys' ability to drive over," O'Driscoll said.
"I think what cost us a bit was we spent a lot of time down in their 22 and only came up with three points in the half," he added. Ireland went into the halftime break trailing 10-3.
O'Driscoll said: "It hurts you a bit when you're going in at halftime, having that many opportunities and knocking on the door and not getting any points out of territory."
Kidney described the dressing room as "very quiet" after the match. Both he and O'Driscoll admitted they had been outplayed by a Wales side who took what opportunities they had and constantly drove the Irish back behind the advantage line when defending. Wales made 141 tackles to Ireland's 93.
"We had high hopes coming into the game and we got outplayed on the day," O'Driscoll said.
"We made too many unforced errors and coughed up some very soft tries and at the business end of World Cup when you get to knockout stage you can't afford to play below par and we did that and paid the price.
"That's the bitter disappointment but you have to suck it up and when you haven't performed on a big stage it's very, very disappointing.
"Collectively and personally, I won't get this opportunity again and that really sucks."