The Wallabies kicked off their tour of the Northern Hemisphere with a hard-fought victory at the Principality Stadium, with Tatafu Polota-Nau, Adam Coleman, Michael Hooper and Kurtley Beale grabbing the tries.
The victory was Australia's 13th successive win against Wales but they were made to work hard for the result, particularly during the second-half, with Cheika praising the character his players showed.
"We had guys come back from injury, and I thought we showed a lot of character out there against a Welsh team that played quite well," the 50-year-old said.
One area of concern for Cheika was the amount of penalties his side gave away, as they conceded 15 during the match, while captain Hooper picked up a yellow card.
"We've got to solve a problem we haven't had all year," Cheika added. "We've not been in double digits (for penalties) for almost all year, so to go 15 in our first game in Europe surprised me - and lose a player, too."
Cheika will be hoping for a much more disciplined performance from his side when they take on England at Twickenham on Saturday.