The Porcupines could not add to their opening day triumph over Aduana Stars after they were undone by a Kwame Boateng penalty in the 34th minute.
The Kumasi-based side finished the match with 10 men after the sending off of Abass Mohammed for stopping a goal-bound shot with his hand, an action that led to the decisive spot-kick.
"I am disappointed with the result," Akonnor told GTV after the game.
"We came here to win or draw. We struggled during the match.
"We struggled because we played the game without a striker and some key players.
"There is a bit of misunderstanding on the way we do things [at Kotoko]. Hopefully we will rectify that and move on.
“We need to improve on the way we handle matches. If we want to get to Africa again, it’s important we win our matches."
Kotoko, currently fourth in Zone A of the novelty league, will take on Eleven Wonders in their next game on Sunday.