Vichai, 60, founder of Thai duty-free giant King Power International, was killed last Saturday along with four others when his helicopter crashed outside the King Power Stadium in the English city of Leicester after a Premier League match.
"It's been a really tough week for everyone", goalkeeper Kasper Schmeichel said.
The Dane said Vichai had had a huge influence on the whole squad.
Gray struck a 55th-minute victor on an emotional afternoon in Cardiff and marked it by removing his top and revealing an undershirt with the words "For Khun Vichai" on it.
Leicester's players had worn white t-shirts bearing Vichai's image and the words "The Boss" on the front of them during the pre-match warm-up.
The game's decisive moment came after 55 minutes when Gray turned home after a fine cross from Ben Chilwell, sparking an outpouring of emotion from the Foxes' players and travelling support after a tragic week. It's been tough. I'm so proud of how everyone played, how professional they were. "We have a very emotional connection with the fans, so we stayed till the end and celebrated victory with them".
Football was a side issue when Leicester returned to action on Saturday but it felt appropriate that Claude Puel's side emerged as 1-0 winners at Cardiff, a week after the death of owner Vichai Srivaddhanaprabha in a helicopter crash.
However, the Spanish worldwide had scored just twice in 20 Premier League games before netting late on in a routine win at Southampton last month.
The team went on to stun the world of football by winning the Premier League title against the odds in 2015-16.
The club's extraordinary run of success played out under Srivaddhanaprabha's ownership.
In the week since the tragedy, the King Power Stadium has been covered in floral tributes left be fans paying their respects, as well as current and former players.
At the Emirates, a superb late strike from Alexandre Lacazette gave Arsenal a point after James Milner, who later broke his nose in a freak clash with teammate Joe Gomez, had given Liverpool a second-half lead.
Mr Vichai had just watched his beloved team draw 1-1 with West Ham United when the accident happened.