The Team of Choice created numerous chances but a brace from Judas Moseamedi was enough to secure a 2-1 win on Sunday afternoon.
"I think it would have been a gross injustice if we didn't win this I must be brutally honest. I thought in the first half we performed extremely well, defensively well structured, well organised, on the transitions we were exceptional," Tinkler told SuperSport TV.
"We should have at least come up at half-time 3-0 up, you know with the easy chances that we had. I explained to the players at half-time that I can't be happy with that. We came in at 1-0 and we left the door open for them. We needed to close that door in the first-half.
"Then we started the second half well, we had at least another two, three great opportunities.I warned them at half-time, they [Kaizer Chiefs] came back with a free-kick where their strength is, equalise. But overall we dominated, we looked like a team that was playing at home but not the team playing away against a massive club like Kaizer Chiefs.
"Today we could have really slaughtered them! I thought at least five or six easy chances, it's not like I'm inventing these chances, clear cut chances. That's my disappointment. But very happy at the end of it all to get a 2-1 win, we're going to the final," he continued.
"[Defensively] we dealt with them, [Samir] Nurkovic pulling out wide, Pogiso [Sanoka] needed to deal with that, sometimes Pogiso was caught with [Lebogang] Manyama as well, there we needed Miguel [Timm] to come and support. I thought we dealt with that long ball fairly decently, it was really on the free-kick that we got caught."
The former Orlando Pirates coach added that he was looking forward to the final against Mamelodi Sundowns.
"I said to the players,"You wanna win this? You gonna beat the best" and now you're playing against the best which is Mamelodi Sundowns. But I've explained to them in this league anybody can beat anybody on any day, it depends how you apply yourself. Today we applied ourselves exceptionally well, that's why we got the result against Chiefs and that needs to be the same against Mamelodi Sundowns."