Jarana resigned last month, citing a lack of support in implementing the turnaround strategy for the loss-making SAA.
On Friday, the board said Jarana would not be serving his three months notice following a mutual agreement.
An acting CEO has since been appointed.
NUMSA's Phakamile Hlubi-Majola says they want Jarana piloting the company.
"Mr Jarana was very good for SAA. He was a man who demonstrated that he genuinely cared about turning the airline around. He worked hand-in-hand with unions to root out corruption," she said.
"Unfortunately, he did not get the necessary support that he needed from the board and government as a shareholder."
"They failed him," Hlubi-Majola continued.
SAA says in a statement that all steps will be taken to give the issues raised the necessary attention.
The Airports Company South Africa says the picket did not disrupt operations at King Shaka Airport.
June 16 is Youth Day and we will be celebrating the efforts and sacrific...East Coast Breakfast with Darren Maule 9 hours ago
East Coast Drive keeps getting better! Check out our new TV ad here.East Coast Drive with Bongani and Mags 1 day, 23 hours ago