The Porcupine Warriors secured a 2-1 victory at the Baba Yara Sports Stadium on Sunday, but the result did little to hide the defensive issues that concerned their South African coach.
Emmanuel Mamah and Isaac Opoku Agyemang put Kotoko two goals ahead before Francis Odoom pulled one back for Heart of Lions from the penalty spot.
Kotoko were also forced to play the closing stages with 10 men after Hamaid Fuseini was shown a straight red card.
Tinkler was pleased to see his side collect maximum points but admitted their defensive performance fell below his expectations.
"I thought today's performance was obviously slightly better than our last performance away from home, but still a lot of work that needs to be done," Tinkler said after the match as quoted by Ghanasoccernet.com.
The former Orlando Pirates coach was particularly concerned by the difficulty his players had in dealing with Heart of Lions' attacking structure.
"Defensively, we were not the way I expect the team to be defensively. We struggled against them with their 4-3-3 system," he said.
"They play with a lot of rotations, no real striker, no real midfielders. Fullbacks very, very high and we struggled to deal with it defensively."
Tinkler explained that his players are still adapting to his tactical instructions, especially when it comes to defensive movement and positioning.
"When to track, when to follow, when to step out of the line, all of these things. Players are still learning, you know, and our shifting today wasn't great even after I moved to a back five," he explained.
The Kotoko coach also urged his players to become more disciplined when they take control of matches, warning them against giving opponents opportunities to fight their way back.
"We managed to survive and create a few opportunities of our own to find ourselves leading by two goals to nil," he said.
"But as I said to the players now after the game, you go to nil up, you can't now start playing around, diddle-daddle with the ball. You've got to be professional, because a team like this, anything can happen in the space of a minute."
Kotoko now have four points from their opening two matches and will face Samartex away on Sunday.
