Amakhosi fell behind when Celtic debutant Helder Pelembe beat Khune with an unstoppable shot in the 34th minute at Free State Stadium.
Bernard Parker missed a penalty soon after before making amends with a scintilating equaliser from range after the break.
Chiefs will host the return leg at FNB Stadium on August 29.
Khune said: "We told our supporters they were going to see goals. Unfortunately we got one and missed a penalty. If we could have converted that we could have taken home a comfy lead.
"It's just unfortunate and we have to go back to the training field and work hard on scoring and keeping clean sheets."
Meanwhile, the Bafana Bafana international is pleased to be back in the number one jersey at Naturena after recently signing a new contract with the club.
Khune made his return at the expense of Reyaad Pieterse in the goalless League draw with Chippa United last weekend.
"Like I said last week, it's good to be back and playing again," Khune said.