The Bantams - with one eye on Sunday's Capital One Cup final against Swansea - controlled much of the game and took the lead through Garry Thompson just before the hour after an error from Dons defender Alan Bennett.
But with the match approaching its conclusion, substitute Jack Midson equalised in the 83rd minute, before Gary Alexander headed in a Toby Ajala corner in the third minute of stoppage time.
"Ultimately the character the boys showed was excellent," said Ardley, whose side are still bottom of the table on goal difference.
"Alan Bennett obviously slipped for the goal but he didn't fold after that he kept going, he dug in and that shows the character of the guys.
"I didn't think it was our best performance by a long way but I don't think against a very good team in Bradford either goalkeeper was worked much during the game.
"After the goal we lost our way a bit, we left spaces but we kept going. I stayed positive, I kept on trying to encourage the boys to push on.
"Football's a cruel game it can kick you in the proverbials. We've just got to enjoy today and get focused again, ready to go on Tuesday.
"I thought the three substitutes did really well, Jack Midson was on the move and looked excellent, Kevin Sainte-Luce showed glimpses of what he can do and Pim Balkestein was solid at the back.
"Overall we'll take it. Yes we can play better and hopefully we will Tuesday but we'll take it for now."