The Whites hit the front on three minutes with what Cowley described 'outstanding' goal from Luke Ayling and doubled their lead in the second half through Patrick Bamford.
Cowley was pleased with how the Terriers reacted to going behind so early.
"We actually started the game well and then conceded an outstanding goal," he said.
"When you come into a game as an underdog, I've won lots of matches like that, you probably can't afford to concede a goal of that quality. It's a great strike and a tough moment.
"When you're a very young team, our front six, take Fraizer out, the others are 18, 19, 20, 21, I was pleased with how we responded. We were able to compete with Leeds, we were able to get some turnovers high up the pitch and disturb their rhythm. We had Trevoh's chance, you probably have to take that if you want to get anything at Leeds. We didn't."
For Huddersfield to get any joy against Leeds' unique man-to-man marking system they needed to be clever in possession under pressure, said Cowley.
"Leeds play an aggressive system. You have to try to hurt them in the space behind, because they suffocate you in a one v one moment, they're all over you. Probably didn't play out of pressure as well as we'd have liked.
"But we saw probably the best team in the league playing at the top of their game, they were relentless at times.
"I've managed against Arsenal, Everton twice and Burnley and that was right up there in terms of an opponents' performance. They're our local rivals, our supporters are proud people, we're a proud club but sometimes you have to credit the opponent. They were outstanding."
Cowley wanted his side to give the travelling Terriers something to cheer but insists Huddersfield can learn from what they saw today at Elland Road.
"We are disappointed for our supporters, we wanted to put in a performance they could be proud of, we know how tough it's been for them," he said.
"Once we get through the disappointment there's loads of learning in that, it was a blueprint, their aggressive intent, they had so much purpose. I really enjoyed it in a sadistic way, the heat was on, you feel like you're really living.
"I was fixated on the game. It was painful but it was a great learning experience for us. I was proud that the players went to the end."
There was a moment late in stoppage time when Cowley felt Huddersfield should have been awarded a penalty for Ayling's challenge on Richard Stearman, but he made little of it in his post-match debrief.
"We should definitely have had a penalty, 100 per cent," he said.
"I don't want to hide behind that, when you see your opponent playing really well you should celebrate that.
"Ayling was on a booking, they'd have maybe been down to 10 men, but I'm not sure we'd have deserved it."