Late goals from Moritz Jenz and Liel Abada gave Celtic victory after County have levelled Kyogo Furuhashi’s opener with an Alex Iacovitti header.
After a challenging first half, the hosts posed Celtic problems in the second period and were right in the match until Jenz headed home with six minutes left.
“It’s been a tough week in terms of the work we’ve done off the pitch in terms of the tactical messages I have given them and the footage we have watched,” said Mackay.
“We play in a manner that doesn’t allow us to be carved open because we were playing against a Champions League team.
“We needed to play in a manner that negated what Celtic did. I felt we did that.
“At the same time we needed the belief to, at times, threaten their goal which we did.
“Disappointed near the end that we got to that point and they managed to get the winning goal.
“But overall I can’t be too harsh.
“[Before they scored] was probably the best part of the game for us in terms of little balls in behind.
“Their goalkeeper [Joe Hart] was smashing things sideways and there were throw-ins into the box.
“I suppose that makes it a bit more sickening.”