And he is confident they will come out in numbers this season to back their team as they prepare for life without Old Firm rivals Rangers.
There will be a serious shortfall in revenue this season and Hoops chief executive Peter Lawwell is hoping season ticket numbers will rise before the new season.
Hay said: "It will be strange for the Celtic fans not having Old Firm games to look forward to.
"But they turn up week-in, week-out to support their team regardless of the opposition and I'm sure that will continue.
"It can be difficult for some people to afford season tickets these days but I'm sure the ones who can will do their bit by renewing their season tickets.
"Every penny counts at this moment in time and hopefully the team can reach the Champions League which will make a big difference.
"However, if the supporters can keep going to games and get behind the team then it will make a huge difference this season."
Meanwhile, Celtic chief executive Lawwell has urged fans to buy season tickets and back the club as they prepare for what he describes as "new challenges".
In an open letter to fans, he said: "As we embark on our 125th season we enter a crucial new phase in the great history of our club.
"Your unwavering support throughout the years has been central to the success of Celtic. It has been one of the core strands of Celtic's DNA.
"There have been great times throughout our history, none more so than Lisbon in 1967 or our centenary year in 1988.
"There have been challenging times too and following recent events, Scottish football and Celtic FC now finds itself on the verge of a new era.
"Throughout our history Celtic has, time and again, stood up for what it believes is right. In recent weeks we have acted accordingly, in the best interests of Celtic and Scottish football.
"More than ever, it is a time to celebrate what we stand for."
The letter continued: "Celtic supporters have already renewed their season tickets in huge numbers.
"I want to thank you all sincerely for your support. You are the lifeblood of the club and it is wonderful that you stand with us at this very important time in our history.
"For those fans still considering renewal or whether to buy a season ticket for the first time this year – we need you back at Celtic Park.
"It is imperative that we continue to develop this exciting young team and give them a platform to take on the best in Europe.
"We now need to make our own history. Let's do it together."