Happy Jele gave Pirates an early lead with a header, but the Citizens got back into the contest courtesy of a Mduduzi Mdantsane penalty early in the second stanza to get the share of the spoils.
Tinkler was pleased with the reaction from his side after going behind and losing Nathan Fasika to injury.
"I thought the performance second-half exceptional but we need to first talk about the first-half. I think a little bit of credit you have to give to Pirates, I think they read our system very well," Tinkler said on SuperSport TV.
"They looked to play [Paseka] Mako very deep, he didn't really play as a wing-back. So he became part of the back-three. They were looking to press us very high.
"He kind of nullified our two strikers in Fagrie [Lakay] exploiting that space in the channel, by him playing that deep. [Vincent] Pule was playing more as a wing-back, than as a winger," he said.
"And in terms of our strategy with pressing, we found it difficult in the first-half and you know they got one good chance with a cross from Pule and we didn't attack the ball, we waited for it and we conceded a silly goal in my opinion.
"But I really think we responded well, [Nathan] Fasika was having a fantastic match, losing him was a big loss because of his aerial ability. But I think when we went back to a four, we started to control the game.
"I really thought the second half belonged, entirely hey, to us. I thought we created the better chances, we got the equaliser and potentially we could have gone on and got the winner.
"We spent a lot of time in their final third, just lacking the end product but proud how the boys responded. Very proud, everyone played, I can't point a finger at anyone. The guys who came in gave it their all.
"And you know what, we'll take the point and go on to this [international] break fairly content with what we have achieved so far."