Cheika hails thick-skinned Wallabies
It helped the Wallabies end their World Cup pool unbeaten and secure a quarterfinal against Scotland.
Wales' failure to breach the Wallabies defence in the 15-6 defeat on Saturday has condemned them to a tough last eight clash against two-time champions South Africa.
Scotland beat Samoa 36-33 earlier in the day to ensure second place behind the Springboks in Pool B.
Neither side managed a try.
Bernard Foley kicked five penalties to get all the Australia points in front of 80,863 people at Twickenham.
Dan Biggar kicked two penalties for Wales.
It meant Australia, who crushed England 33-13 and Fiji 28-13, came through Pool A unbeaten.
However, Cheika was a relieved man after the riveting encounter.
"If they say that behind every good man is a good woman, behind every attack is a great defence," said Cheika.
Australia prevented Wales from scoring at all in the second half even when reduced to 13 men as scrumhalf Will Genia and lock Dean Mumm were both in the sin-bin.
"I'm happy we won, it was a different type of game," said Cheika.
"We had to show a different skin," added the coach, who has been in charge for less than a year following the resignation of Ewen McKenzie.
"There were plenty of imperfections again and it was 13 men only for eight minutes not 80. But the team's been working hard since we got together last year."
Asked if he preferred Saturday's success to the Wallabies' win over England, Cheika replied: "I liked this win because as a forward, and not a very talented one, it was just about getting stuck in."
Australia captain Stephen Moore insisted there was no great secret to the way his side kept Wales at bay.
"The guys just did their jobs," said the hooker.
"It is not complicated."
Wales captain Sam Warburton insisted his bruised and battered side's morale was intact despite the prospect of playing against a resurgent South Africa.
Wales beat the Springboks 12-6 when the teams last met in Cardiff last year.
South Africa are, however, determined to prove wrong the doubters who wrote them off after they lost to Japan in their opening match.
"We've got a quarterfinal against a side we beat last time," said Warburton.
"One thing this group of players doesn't mind is a challenge and that's what great teams are made of," the flank added.
Warburton admitted that the Wallabies were made of stern stuff.
"We threw absolutely everything at Australia and you have got to give them a heck of a lot of credit in defence – they were outstanding," he said. "We were hungry for that try."
"If you spend that much time in their 22, you have to come away with a try," said Warburton.
The Welsh captain admitted his side now have a "tougher" quarter final but remained defiant. "There is no easy way to the World Cup final," he said.
Australia extended their record against Wales to 11 wins dating back to 2009. All but one has been by a single figure margin and Wales coach Warren Gatland said this was another classic.
"It was courageous defence by Australia. They were throwing their bodies on the line," he said.
"It was a tight, tough Test match, not a lot in it. We were held up over the line three times and had opportunities but didn't take them," the New Zealander added.
"But the guys have already turned their minds to South Africa, the focus is purely on winning a quarter-final."
The Wales football team also lost later on Saturday but despite their 2-0 defeat to Bosnia-Herzegovina it still was enough to end a 57 year wait to qualify for a major finals as they reached the Euro 2016 championships.
Agence France-Presse
