SuperSport were held to a goalless draw by the Zambians at Lucas Moripe Stadium in the first leg in Atteridgeville this past Friday.
"There is bitterness and disappointment to be honest because we should be talking about something completely different if certain decisions were different in the first 20 minutes,” said Tinkler.
"I think to a degree I'm not saying it was one sided because there were a lot of errors made by both sides. I think for this level of competition now in the quarter-finals we need to do better.”
The former Cape Town City mentor, however, was encouraged to keep a clean sheet ahead of the return duel at Levy Mwanawasa Stadium in Ndola on Saturday.
"I am happy for the fact that we kept a clean sheet at home and now they will play openly. Obviously they will need to look for a goal. We must take our chances when we get our chances there. It's going to be a tough trip. They are a good team and well structured by the coach,” concluded Tinkler, who guided Orlando Pirates to the final of the continental competition in November 2015.
Matsatsantsa next host Chippa United in the Premiership on Wednesday night (19h30). Tinkler's charges have picked up six points from three league games - two more points than the Chilli Boys.