The athletes entered Carrara Stadium before the broadcast began and spent most of the ceremony cloaked in darkness as Beattie and a number of other dignitaries took to a stage to shower praise on the April 4-15 Games.
Local media slammed organisers for taking the spotlight away from the athletes, and Australia's para-athlete flagbearer Kurt Fearnley said it was "pretty strange".
Beattie said organisers had intended to spare athletes a long wait before entering the venue but had got the broadcasting decision wrong.
"The last thing they want is standing in a field for an hour waiting to get into a closing ceremony," Beattie told the Seven Network's 'Sunrise' breakfast show on Monday.
"That was clearly a stuff-up. Now, I'm sorry, if I get a chance I'll apologise to Kurt (Fearnley) this morning.
"Should they have been part of the actual ceremony that was broadcast? Of course, they should have been."
Images of joyous athletes filing in behind their nations' flags have been a feature of closing ceremony broadcasts at Commonwealth and Olympic Games for decades.
"If you do it and it doesn't get covered on telly, does the tree actually fall? I don't know. It was pretty strange, but what do you do?" Fearnley, who won gold in the T54 marathon, told state media on Monday of the broadcast snub.
"I got to carry that flag around, and thankfully my mum and my sister were in the stadium. They did see that moment.
"I'm not going to let anything even slightly taint what was an incredible day."
Social media users also criticised the opening ceremony for being too long and featuring too many speeches.
"The speeches were too many and too long. I was part of that and I acknowledge it. Again, we got that wrong," Beattie tweeted.
"It is very simple. I should not have spoken."
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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