The star batsman was fuming after the incident as he travelled to Australia to play for the Melbourne Stars in the Big Bash League after his Dolphins side lost in the final of South Africa's Twenty20 competition on Saturday.
"I suggest you tell Platinum, First Class fliers that they not allowed in your lounges with flip flops before they fly, @Qantas! Muppets!," he tweeted to his 2.88 million followers.
"And BTW, @Qantas! Thongs (flip flops) are an institution in this great country! GET A GRIP! Tired, jet lagged & just wanted to chill! #Muppets."
"@KP24. It must have been disappointing Kevin. Changes from earlier this year. Hope to welcome you back again soon," Qantas tweeted in response.
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An airline spokesman told AFP Tuesday that "we reached out to members early in 2015 to remind them of the dress standards and had a grace period up until April this year".
"We completely understand that being declined at the door isn't a great experience, so this is a good opportunity to remind those wanting to use our capital city lounges of the dress code that applies," he added.
"Anyway, it's soooooo cool being back in Aus! I know so many wonderful people here! Can't wait to see you all over the next month!," he said.
The Twenty20 Big Bash League starts on Thursday.