Mackay saw Peter Whittingham and Joe Ralls go closest for Cardiff but despite missing out on all three points, the Bluebirds boss was far from disappointed.
The result leaves Cardiff in the promotion hunt after Mackay's men avoided defeat at a club where they have not won at in 29 years.
Millwall will feel upset they also failed to pick up three points as James Henry saw his first-half header strike the woodwork, while Darius Henderson was off target for the Lions late on.
"That's four clean sheets in a row now," said Mackay. "We knew we were coming here and expecting a tough game - it's always a tough game here.
"Kenny's a good manager and he has got an experienced team here.
"We knew there would be physicality to the game which we would need to match and we did.
"I thought first half we kept a lot of the ball without doing much with it in the final third.
"Second half both teams had a couple of chances and overall it was a real good tough point.
"It was one of those days where you go home and say it was probably honours even."
Millwall came close to scoring when Jay Simpson won possession and played the ball in for Liam Feeney.
His low cross found James Henry with a sight of goal but the midfielder's shot crashed back off the woodwork.
Hamer Bouazza's effort 15 minutes from the end flew wide of the post, while Henderson had a chance to win it for Millwall but his header bounced over the bar.
Millwall manager Kenny Jackett said: "I thought it was a very technical game as a lot of games in the Championship are now.
"It was a tight game but I think we need to find five, maybe 10% if we can, which will help us progress up the league.
"It's not a bad point - any time you add to your total it's not a bad point.
"There are a few things we'd like to improve on - particularly our confidence and doing a bit better when we get into good situations.
"We finished ninth in the division last year and I think up until two games to go, we were in with a shout of getting into the play-offs.
"Things have been tight though this season - we've had many tight games - and we have been tight defensively. We just need to improve on getting goals from all areas."