The Terriers were without Tommy Elphick, Danny Simpson and Jaden Brown for their first league outing since the international break.
Cowley opted to deploy midfielders Lewis O'Brien and Juninho Bacuna in the full-back spots while Jon Stankovic partnered Christopher Schindler in the centre of the defence.
Huddersfield took the lead through Fraizer Campbell on 55 minutes before being pegged back by Lukas Jutkiewicz's goal with just over 10 minutes remaining.
"In 13 or so years in football management, after about 800-odd games, that's probably the toughest team that I've had to select," said Cowley.
"To lose three of your back four in what is already an unbalanced squad, has made it very, very difficult.
"But I have to credit the players, particularly the ones playing out of position. When you consider all that, it was a lot to contend with so credit to them."
Cowley was proud of the performance from his side, who will have been frustrated not to take all three points after creating the better opportunities.
"My over-riding feeling is I'm really proud of the players' efforts. They showed a lot of fight today," he continued.
"A lot of our defensive work was really good and Birmingham didn't have a lot of chances at all.
"If you want to be a successful team then you have to concede less than a goal a game - that's less than 46 in a season."
Huddersfield have now picked up 17 points from their first 17 outings.
And Cowley first wants to reach 50 points this season, a total he feels is enough to keep the Terriers in the Championship.
He added: "We want to get to 50 points. Once you do that, you can re-define your objectives."