The 32-year-old Thaiday was considered instrumental in helping rebuild the Kangaroos culture, including the penning of an ode during last year's Four Nations tour in Europe. Despite playing in the mid-year Test against New Zealand, he was dropped from the Queensland State of Origin team after their game one loss.
The Maroons won the last two games to claim the series, however Meninga insisted it was still an oversight to not speak to him.
"I put my hand up. There's no excuses for that," he said.
"I agree with his comments and part of what I wanted to achieve around the Kangaroos was around the rise and part of that respect.
"I just forgot. That's not an excuse. I should've shown respect. He's been a warrior for the big game in general and he needed that respect."
Meninga and Thaiday have a long history dating back to when the former Maroons coach handed the Broncos second-rower his Origin debut in 2006.
He hoped the phone call would save their relationship.
"I hope that he appreciated the phone call," he said.
"He vented, I understand that too. He's had a tough year, particularly representatively. He had every right to vent.
"I phoned him because I was deeply apologetic and didn't show him the respect he deserved."
Asked how close Thaiday was to selection, Meninga said: "That's not for me to comment publicly on to be honest with you.
"We're talking about the incident. I fully support Sam's comments and I can't be more sorry."
Thaiday's omission is likely to end a 10-year career in the green-and-gold jumper dating back to 2006 totalling 34 Tests.
