City scored in the opening 10 minutes and held on to narrowly beat Amakhosi 1-0 at the Cape Town Stadium on Friday evening.
Tinkler revelled in his team's display as they stuck to their guns to ensure their passage to the next round of the competition.
"I'm obviously very proud of the boys. What was important for us was to be disciplined defensively; organised; structured," Tinkler told SuperSport after the match.
"We knew that they would be looking to come at us, and i thought we defended exceptionally well today and then, obviously, Shuaib [Walters] was fantastic in goal for us."
The former Orlando Pirates tactician, who continued his unbeaten streak against Chiefs, felt his side could have scored another goal but was pleased that they used their opportunity on the counter-attack.
"I knew we would get chances on the counter and on the break, and they had the corner and we got the goal and could possibly have even had another one just before half-time," he added.
"Second half we started to defend a little bit deeper but you can understand that because the boys got a little bit nervous and cagey.
"But defensively I thought we were solid. Once or twice we looked to hit them on the counter, but ja, I'm very proud of the boys."