Puel's side played out a 0-0 draw with Burnley on Saturday, unable to find a goal to add gloss to a day when the club and the city paused to pay tribute to Vichai, who was killed in a helicopter crash outside the King Power Stadium on October 27.
Leicester returned to action with a win away to Cardiff last week before Puel and a number of players attended Vichai's funeral in Thailand but the Burnley game was their first home fixture since the tragedy, which also killed four other people.
Grief-stricken fans marched in their thousands through the rain to the stadium before a series of tributes to the much-loved chairman before and after the match.
Puel spoke of his pride in his players after the draw that leaves the former champions in 10th spot in the Premier League, saying they found the right balance between emotion and a professional attitude.
"Of course it was a special day, a special, special match," he said. "It was our first game at home after the awful accident.
"I think it was important to have this communion with our fans and to give our best to honour our chairman and I would like to say I'm proud about my players, about their performance, about their mentality in this game."
But the Frenchman must now work out a way of helping his players through the next period of the season after the raw emotion abates and the cascades of tributes are cleared away.
With his vast investment and boundless enthusiasm, Vichai was the inspiration for Leicester's incredible Premier League title triumph as 5,000-1 outsiders in 2016, an achievement that will stand forever as the highlight of his eight years as owner.
Title-winning manager Claudio Ranieri was on the pitch at the end of the match on Saturday as players, staff and Vichai's son Aiyawatt, known as Top, walked round the pitch, waving to fans, who responded with chants of "Vichai".
Puel said he felt a connection to the title win, with Ranieri on the pitch.
"To see the former players, former managers come back to honour the chairman shows the man he was," he said.
"He was generous with his feeling," he added. "He was always with a smile. Always he wanted people happy around him."
Puel was asked whether it was possible to bottle the feeling of solidarity at the club and use that to propel the team forward for the rest of the season.
"I think our desire in the club, with our fans, is to continue his way, of course, his dream, his work. He changed a lot the life of people in the city, in the club and all people want to continue to perform for him and for his family.
"After, it will be important every time, every game to play full games with this intensity, with this mentality but it will be hard work in training sessions because we can't play for example until the end of the season just a game with emotion.
"We need to have his dream in our heads but also professional attitudes, every day hard work in the training sessions all the time and to give our best."
And he said that the international break -- with Leicester's next game not until November 24 -- would benefit the players and allow them to focus on training again after a difficult two weeks.
He added: "For all the international players it will be a possibility to play with other teammates, I hope to think other things with their national team and I hope they will come back with... a good rest for their head."