The Bluebirds on Friday face Blackburn, whose Indian owners the Venky's Group have come under fire from Rovers fans.
Mackay says he has a good relationship with his own club's Malaysian owners and the game has to adapt to changes.
"It's the way it is, the way it's going and it's how you manage that," said Mackay.
Cardiff City's owners upset a some supporters in June when they announced the team would play in red rather than their traditional blue.
The club's owners said the rebranding was part of "major and significant" investment which would also expand the club's appeal.
Cardiff have yet to lose at home in their new red kit and are top of the Championship.
Mackay believes that the game has changed, and one of the roles of managers is to adapt to those changes.
"I think it's different than what used to be the norm of the local board of directors and a couple of local businessmen people... dyed in the wool supporters for the last 50 years," said the Scotsman.
"I think the whole of football is adapting to that.
"Managers have to adapt the most because they're the people that have to deal with the owner on a day-to-day level of managing the football club."
Mackay, who succeeded Dave Jones in June 2011, says he is very happy with the way his relationship with the club's owners has developed.
"What you hope is that there's transparency and you hope that your message is able to get through in the way that you said it, as opposed to going through Chinese whispers and end up getting to the owner in a different way.
"I've made sure that's absolutely not the case, I've had a real good chief executive in Alan Whiteley for the most part here and before him Gethin Jenkins. There was a real good trust in the relationship.
"From day one my chairman TG [Dato Chan Tien Ghee] has been on the phone to me once a week and more recently he's been much more visible.
"The main thing for me is the fact that the plans that you put in place... the decisions that I take and reason I take them go straight to the people that are owning and running the football club, and that's the crux of it."
Rovers were relegated from the Premier League at the end of last season and are lying in ninth place with new manager Henning Berg in his post barely a month.
And Mackay expects Blackburn to present one of the toughest tests so far this season at Ewood Park on Friday night.
"I suppose there's been a lot of chopping and changing at the club, a new manager coming in, different players coming in and a team coming down from the premiership so there's a big mix of things going on there," said Mackay.
"I think once things settle down at Blackburn then they've got a squad that can certainly progress in this League, so it's going to be a dangerous one for us."