Pay-per-play signing Kieron Dyer stabbed home his first league goal in six years for an early opener and Sammy Ameobi, who arrived on loan from Newcastle, cracked in a sizzling second soon after to put Boro in control of a dominant first half.
But Cardiff hit back after the break and pulled one back through Aron Gunnarsson before creating chances to level in a frantic finale.
"I felt we probably deserved a point on the basis of that second half performance," Mackay said.
But he admitted the Championship leaders had been the architects of their own downfall.
"We shot ourselves in the foot a bit and we gave away two goals which we would normally never concede and that made it very difficult.
"But we put in a spirited second half and we got one back and to be honest we had enough chances to have got the leveller."