Flanker Sean McMahon scored two tries in a man-of-the-match display at Villa Park, while fellow back-row forward Ben McCalman and wing Drew Mitchell also touched down twice.
It was the biggest win of the tournament so far, yet Cheika insists the Wallabies must find another gear for a trip to Twickenham that will go a long way to deciding Pool A.
“We are going to have to improve on the first two matches to be able to compete with England,” he said. “England are the home team and they are going to be the favourites.”
Australia failed to pick up a bonus point in their opening 28-13 win against Fiji but made 14 changes and looked keen to make amends, McMahon crossing for his first after just seven minutes.
Uruguay’s thrashing might have been even more chastening had Australia fly-half Quade Cooper not missed six of his conversion attempts and incurred a third yellow card in two months.
Despite Cooper’s visit to the sin-bin, the two-time winners made the bonus point safe before half-time with further tries from wing Joseph Tomane, lock Dean Mumm, centre Henry Speight and McCalman.
Australia cut loose after the interval, with centre Matt Toomua and replacement Tevita Kuridrani also crossing and Mitchell becoming his nation’s leading World Cup try-scorer with 11 – just three behind New Zealand great Jonah Lomu’s all-time tournament record.