The Bluebirds will make their Barclays Premier League bow at West Ham on Saturday, 51 years after their last top-flight outing.
Malaysian businessman Tan vowed to back his manager in the transfer window after the club secured promotion back in April, and he has been true to his word.
The acquisitions of Danish striker Andreas Cornelius, Tottenham defender Steven Caulker and Sevilla midfielder Gary Medel have each raised Cardiff's record outlay, while John Brayford and Simon Moore have been brought in from Derby and Brentford respectively.
Tan has made it clear he expects to see a return on his investment, with Mackay still looking to make further additions to his squad.
But the Scot is comfortable with the pressures that go with his level of expenditure.
"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."
He added: "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."
Mackay is set to hand 18-year-old full-back Declan John a full debut with Andrew Taylor suspended, while Cornelius is doubtful after picking up a knock in training last week.
But Caulker and Medel, who trained with his new team-mates on Friday, are in line to make their Cardiff debuts against the Hammers.
Chile international Medel arrives with a reputation as an uncompromising midfielder, having been sent off seven times in 90 games for Sevilla in La Liga.
But Mackay is confident he has landed a man who will be an integral part of his Cardiff side, and believes he can be an important presence at Upton Park.
He said: "He is very experienced for someone who has just turned 26.
"He's got over 50 caps for Chile. He's played in the Boca Juniors v River Plate derby, one of the most frenetic derbies in the world.
"He has played in La Liga against top, top players. In February Xavi came out and asked Barcelona to try and buy him so that is pedigree for you.
"I believe he also thinks he should be on the top stage as well and that's important.
"It's important to have players that think they belong standing in the middle of Upton Park in the Premier League.
"He's a leader and an organiser and we are delighted to get him because we worked very hard on it."
Cardiff have also submitted a planning application to local authorities for phase one of the planned development of Cardiff City Stadium.
If successful the process will add a second-tier to the ground's Ninian Stand and increase the capacity to approximately 33,000.
- Sports & Recreation
- Andreas Cornelius
- Gary Medel
- Barclays Premier League
- Steven Caulker