City were on the backfoot for large periods of the first half but fought back valiantly to take the game to extra time and a penalty shoot-out, where they missed five of their seven to lose the tie in heart-breaking fashion.
Tinkler expressed sympathy for his charges after shoot-out, where they only managed to convert twice.
"I feel for the boys. Tough to lose it like we did. A penalty shoot-out is always Russian roulette. You can train all you want. We practised penalties three days solid. When you put them in this situation, people melt. Unfortunately, the pressure was big and you can't replicate that in the training sessions," the City mentor told SuperSport TV. "
"Congratulations to Sundowns, exceptional team. Difficult team to break down. I thought we defended quite well but they have so many clever players in their team. They found solutions and created opportunities. We found it difficult to contain them.
"The boys responded well. We needed to be patient on the ball and not panic. There were periods where we started to panic. We changed the formation and started to control the game and maybe could have gone on and won it. That all changed when Fasika got the yellow card and then we just had to hang on.
"We needed to press a bit higher. Their movement was hurting us in between the centre backs. [Themba] Zwane was a constant threat every time he found the half spaces. So I thought it was important to change to a back three so we brought Terrence on and I think that made a big difference.
"We started to find each other with a lot more ease which led to us getting the equaliser so the changes we made an immediate impact."