Australia, playing their third match in successive nights, lost Nick Kyrgios to a collarbone injury before the quarter-final and faced a Canadian team who has a day off on Wednesday.
"The scheduling is a big problem," twice Grand Slam champion Hewitt told reporters.
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"You know, for us to have had to play these three nights in a row, it's not ideal.
Yeah, I understand it's the first time and you're going to have hiccups and you've got to learn from it. But there's been a lot of small problems, that's for sure.
After a two-month break, Kyrgios had been in fine form in Madrid, bashing down 22 aces in a straight sets victory over Steve Darcis late on Wednesday to help Australia beat Belgium and reach the last eight.
But the 24-year-old pulled up sore on Thursday and was replaced by Jordan Thompson, who lost in straight sets to Vasek Pospisil in the opening singles rubber.
"I think (the injury) was similar to what he had at Laver Cup time," Hewitt said of Kyrgios' collarbone problem.
"That's just the way the cards fell. It's been pretty tough I guess trotting back out the last three nights as well.
"To Johnny's credit, he went out there and left it all out on the court."
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Hewitt has been a vocal critic of the revamp of the 119-year-old tournament that originally had home and away ties played throughout the year.
Defeat, however, was no less difficult for the 38-year-old, who holds Australia's record for Davis Cup ties and wins as a player.
"I think in any kind of format that I've ever seen anyone play for their country, they go out there and leave it all out there," he said.
"The format changed but we still came here to give absolutely everything we could, and we did that.
We're all hurting at the moment. But it just shows that it means something, which is good.