Mackay saw his side go behind in just the second minute of the game when Charlie Austin headed the Clarets into the lead, but he was happy with the way his side fought back to earn a point.
He said: "Overall it was a good point and a hard battle. We lost a goal very early on and had to be patient and calm. I think that the way we played and to get a goal back in the first half through some impressive play, we can be happy to come away from Burnley with a draw.
"It's not the win we are looking for, but I'm happy with the attitude of my players to keep fighting after a bad start.
"Against Brighton last week we didn't play particularly badly, we just gave away three bad goals. So today to come back from that, especially after going behind so early and to impose some shape in the game, we have to be happy.
"As said, I'm pleased with the application of my players, particularly after many of them having played a lot of games over the last fifteen days. It shows a measure of the spirit here.
"I'm also pleased for Earnie. Today marks his 200th career goal and it's a habit that he's got that's hard to come by, to be at the right place at the right time. It's a fantastic achievement and the reason we brought him back here."
Burnley boss Eddie Howe felt it was an improvement on the previous games this season and that his side are very much heading the right way.
"I take a great deal of heart from that performance," he said. "I thought we were excellent today. In the first half hour we were really positive, got the ball wide and crosses in from the flanks.
"On another day we could have been more than one up and the disappointing thing from our view is that even though we are not conceding a lot of chances to teams, every chance the opposition get they take. Lee Grant has had nothing to do again and yet he's picked the ball out of the net.
"It was a soft goal and we need to eradicate that form our play. We are working towards that and I thought we looked solid today.
"There's still hard work ahead of us, but we are moving in the right direction."
He continued: "We didn't quite hit the same heights in the second half and credit to Cardiff. They changed their system three or four times to try and live with us and in the end they got a system that nullified us out wide.
"We couldn't get the ball out to Keith and Ross and Charlie was struggling after being smashed on the touchline. Up until that point he had been outstanding, but I thought it was a bad tackle and that knocked him and he was struggling after half time.
"In the end we were the only team trying to win the game, but we just couldn't break them down."
Finally, he explained his decision to replace Andre Amougou with Michael Duff in the centre of defence. He said: " I just felt we needed that tactical change. Michael is a fantastic talker. He's an experienced player and he will help the young lads. I thought he performed really, really well and he can be pleased with that performance."