But Australia's vice-captain said the controversial incident strengthened the case for reviews to be left solely in the hands of the umpires.
Broad had made 37 in England's second innings when he nicked a ball from teenage debutant Ashton Agar via Haddin to Australia captain Michael Clarke at slip but was given not out by umpire Aleem Dar.
As Australia had used up all their reviews in this innings they were unable to challenge Dar's verdict, even though replays showed a thick edge.
Broad went on to make a further 28 runs, before he was out for 65, in a match England won by just 14 runs.
West Indies great Michael Holding said Broad should be banned from the second Test at Lord's starting Thursday over his refusal to walk.
But Australians have traditionally waited for the umpire's decision and Haddin said Tuesday: "I personally think the umpires might as well use the reviews. I don't think they need to be in the players' hands, to be honest.
"I see nothing wrong with what Stuart did.
"The umpire is there to make the decision and he has seen it different to everyone else."
Haddin added: "That's what the system was brought in for, the howler. The system is the same for both teams, we just haven't used it very well.
"That's the bottom line.
"We have to take emotion out of the decision and go on what we see. If you think it's out, challenge it.
"We obviously got it wrong this Test but it might be different next Test."
Haddin took Australia to the brink of a sensational win, scoring 71 before he was last man out on Sunday, caught behind by opposing wicketkeeper Matt Prior off James Anderson, who took 10 wickets in the match.
However, England needed to review the original not out decision before Haddin was dismissed.
Haddin admitted Tuesday he'd got an edge.
"The umpire didn't give me out so I wasn't walking," explained Haddin.
"I knew I nicked it. I told James (Pattinson) that I hit it.
The umpire just didn't give me."