The Brumbies defended as a unit, making over 200 tackles – three times more than the Stormers – while they also forced 10 turnovers against a hapless Cape side.
But City’s 10th Premier League in a row came at a price with key midfielder Kevin De Bruyne forced off with what looked like another knee injury in the 38th minute.
Liverpool defender Virgil Van Dijk joins team-mate Sadio Mane on the list, while City forward Raheem Sterling is included alongside team-mates Sergio Aguero and Bernardo Silva.
Klopp said his players have benefited from the experience of reaching the Champions League final as well as securing a Premier League top-four finish last year.
City’s quadruple bid ended when they went out of Europe on the away goals rule on Wednesday, despite winning 4-3 win at the Etihad Stadium, after the two-legged quarter-final tie finished 4-4 on aggregate.