Ms Soundararajan has also issued a notice to the officials concerned.
An event where the guests of honour were sitting on the floor while the officials honouring them were occupying most of the chairs has sparked a controversy in Puducherry.
The Tribal Day Function organised by the Puducherry government on the occasion of tribal icon Birsa Munda's birth anniversary on Wednesday was attended by the Union Territory's Lieutenant Governor, Tamilisai Soundararajan, Chief Minister N Rangasamy, Speaker Embalam R Selvam and several senior officials.
Videos showed a section of tribal men and women sitting on the floor along the aisle. Some people were also seen walking out in protest. One man was heard saying, "They spent Rs 3 lakh on this function. They could have built three houses for tribal families instead."
Another tribal man said, "You brought us here saying we will be given awards and this is how you treat us? This is humiliating."
After videos of people sitting on the floor went viral, the Tribal Welfare Department, which organised the event, was slammed for insulting tribals. Several people on social media criticised what they called a "lack of social justice".
Ms Soundararajan said she had asked for chairs to be arranged as soon she found out. She has also issued a notice to the concerned officials.
"Soon after I learnt about it, I asked officials to arrange chairs for the people sitting on the floor. Officials say they had made proper arrangements. I believe it is not right even if one person was disrespected. I regret this. How can this happen in my administration when I had arranged chairs even for children at earlier events? This shouldn't have happened," the lieutenant governor said.