Pirates beat Al-Ahly 5-3 on aggregate on Sunday to qualify for the CAF Confederation Final for the first time in their history.
The Buccaneers were warmly received by supporters at OR Tambo International Airport on Tuesday afternoon.
“The reception is fantastic," Tinkler said.
"I want to thank Pirates fans and the South African fans for the support shown throughout the competition.
“I am very proud of our achievement in getting the win. It was a good long trip back home and to get this kind of welcome is the icing on the cake.
"We are very proud of what we achieved and want to thank everyone for the support."
Tinkler also showered praise on his players for their spirited efforts.
“I am very proud of the boys for a gusty performance. They showed a lot of character and the plan worked out in our favour.
”We always believed that as long as you can get an away goal, the tide will turn in our favour and we always believed we could do that.”