The 27-year-old caused an uproar during the Three Lions' second innings of the opening match of the series when he refused to declare himself out after edging the ball to slip into the wicketkeeper's glove.
Australia had by then used up their two permitted DRS options with the umpire deeming the incident as not out, as they went on to lose by 14 runs on Sunday, but Flower does not feel that Broad deserves to be punished for his actions.
"Stuart Broad, like every other batsman in international cricket, has the right to wait for the umpire to make his decision," Flower told the Nottingham Post. "The umpire's job is to make those decisions."
The second Test starts at Lord's on Thursday.