The Bluebirds have not been in England's top division in 51 years but head into the season having broken their transfer record three times and spent more than £25million on improving their squad.
Malaysian businessman Tan vowed to back Mackay when Cardiff secured promotion back in April, and he has been true to his word, but Mackay is comfortable with the pressures that go with that kind of outlay.
The original record breaker Andreas Cornelius might miss their opening game against West Ham on Saturday but former Tottenham defender Steven Caulker and Chilean midfielder Gary Medel should be available.
"He (Tan) has expected results from last summer," he said. "When I was offered the job, it was a three-year plan.
"His task for me was to be promoted last summer. That's expectation, that's pressure, so I have had that. Football managers are under pressure every week.
"I've broken the transfer record three times, but it's where we are as a club. It's not about looking back, it's about making sure we keep striving to push forward.
"The club has come a huge distance in a short space of time relatively with help from a lot of people over a long period to get us to this point.
"But as far as myself and my staff are concerned, we want to keep striving and make the club better in terms of facilities, the staff we bring in and the players we bring in and we have to try and get the best players here.
"I won't apologise for that and I will take my time and do it in the way I think is best for this football club. It was never going to be about quantity this summer, it was always going to be about quality.
"That takes patience and it takes being criticised (for a lack of activity early in the summer), that's fine because at the end of the day I know exactly what I want and how I want to go about it."