Turner is also convinced that their former manager would want his players to move on quickly from his departure.
Mackay, who brought the majority of the current squad to the Welsh capital, was dismissed on Friday as his civil war with controversial owner Vincent Tan reached its inevitable conclusion.
The Scot did not get a chance to say goodbye to his players, but their performance during the first hour of the 2-2 draw with Sunderland on Saturday perfectly emphasised the Bluebirds at their best under their former manager.
Goals from Jordon Mutch and Fraizer Campbell gave Cardiff a thoroughly deserved 2-0 lead, only for late goals from Steven Fletcher and Jack Colback to earn Sunderland a share of the spoils.
The result leaves Cardiff two points and two places above the bottom three ahead of the New Year's Day trip to Arsenal.
And centre-half Turner knows the squad cannot afford to dwell on events of recent days and they must follow the example Mackay set them.
"We have to move on," he said. "If we don't then we will get relegated. We have to look forward. It's what we want to do.
"That's the one thing the old manager would say, once the game is over look to the next one.
"Whatever's happened, you focus on the next challenge. So we want to look forward and he'd have wanted us to look forward and carry on. We are at the halfway point and we have a good chance of staying up."
But Turner admits the players have found it difficult to take in that their boss has lost his job
"We have not had time to digest it yet because with the Christmas fixtures they are coming thick and fast and we have had to concentrate on the game.
"I think we approached the Sunderland game in the right manner, as we would have regardless of what's been going on around the club.
"Maybe now we will have time to digest what's actually happened over the last few weeks and then we move on to Arsenal away.
"The manager brought me here and showed a lot of faith in me, but at the same time nothing is forever in football and you have to look forward."
"Obviously we are going to have a manager come in at some point so until then we are very comfortable with the staff we have here and we are uncomfortable with what's going on.
"It's not a problem that we did not get to say goodbye to Malky because it's a free world so you can speak to who you want so I can speak to him anyway. I am sure I will speak to him."