Inglis was stripped of the Australian captaincy on Tuesday after he was charged the previous day with drink-driving and speeding offences.
Meninga said Inglis was "bitterly disappointed in himself more so than anything else".
"He stuffed up. He has made a poor error of judgement and he has paid the price for it," he said.
"I want to see Greg have a strong off-season and start the season well for the Rabbitohs. He will lead Queensland again next year."
Meninga added he would then wait and see when the national team plays next whether Inglis would become captain.
"He was really disappointed in himself but in the true character of him he has taken it on the chin," he said.
"The ultimate lesson in all this is you don't get behind the wheel of a car under the influence of alcohol."
Meninga flies out of Brisbane on Thursday with the Prime Minister's XIII squad to prepare for Saturday's clash with Papua New Guinea in Port Moresby.