Aiyawatt laid a wreath with his mother Aimon at the stadium on Monday while they also viewed messages, floral tributes, shirts and scarves laid in honour of the founder of duty-free King Power International, who was a huge favourite among the Leicester supporters.
"I would like to thank everyone from the bottom of my heart for this overwhelming support," Aiyawatt said in a statement.
"Thank you, also, to Leicestershire Police and the Emergency Services. Their fast response on Saturday kept a lot of people safe. Their professionalism and sensitivity since then have made the last few days as bearable as they could be.
"What happened made me realise how important my dad was to many people all over the world and I’m touched by how many people kept him close to their hearts."
Vichai bought Leicester City in 2010 and went on to stun the soccer world by beating odds of 5,000/1 to win the Premier League title in 2016 in what amounted to a sporting fairy tale.
"I'm extremely proud to have such an extraordinary father. From him, I have received a very big mission and legacy to pass on and I intend to do just that," Aiyawatt added.
"He loved his family. He made Leicester City into a family. And nothing would make him prouder than to see how the Leicester City family that he built is supporting each other through a time of such sadness."
After completing forensic enquiries, Leicestershire Police have formally identified Vichai as one of five people killed in the helicopter crash.
"Formal identification of the four other people, who are believed to be Nusara Suknamai, Kaveporn Punpare, Eric Swaffer and Izabela Roza Lechowicz, is still being actively progressed," the police added.
Leicester confirmed Saturday's league match at Cardiff City would go ahead as scheduled after Tuesday's League Cup game with Southampton was postponed following the accident.
(Reporting by Hardik Vyas in Bengaluru; Editing by Alexandra Hudson)
