Pirates handed AC Leopards a 2-0 beating at the Orlando Stadium on Saturday evening to put themselves in a good position to finish top of Group B ahead of Zamalek.
The Buccaneers are currently three points ahead of their Egyptian rivals, who have a game in hand against CS Sfaxien on Sunday.
Pirates still have to travel to Cairo to meet Zamalek in their final group fixture, where a win would see them going into the semifinals with a top seed advantage.
It has been a similar showing from the Soweto side that saw them going the distance in the 2013 CAF Champions League.
However, Tinkler says his team are not favourites to go all the way this year, insisting that their anticipated opponents are all capable of winning the tournament.