Incoming Celtic chief executive Dominic McKay must bring instant success and will not be given time to settle, according to Paul Lambert, who also says it "doesn't matter" who replaces Neil Lennon as manager at Parkhead.
McKay, currently the Scottish Rugby Union chief operating officer, is due to replace Peter Lawwell on July 1 but many believe the change needs to be made now following Lennon's resignation and the collapse of Celtic's 10-in-a-row bid.
He will be expected to lead the hunt for Lennon's successor when he takes over, while a behind-the-scenes restructure means the recruitment of someone to fill a director of football role will also be high on McKay's to-do list.
- 'Director of Football critical for Celtic'
- How can Celtic rebuild after Neil Lennon?
- Scottish Rugby warn Dominc McKay won't join Celtic early
"Rugby is a totally different sport," former Celtic player and Ipswich Town boss Lambert told Sky Sports. "If he thinks he will go in there and get applauded from everybody, that doesn't quite work in the Glasgow goldfish bowl.
"He's going to have to hit the ground running. He's going to have to win. Peter Lawwell did a fantastic job [in that role] over the last few years.
"At Celtic, you have to win. It doesn't matter if Barcelona, Manchester United or Manchester City came to town tomorrow. The fans expect you to win. Some people can't handle it. Can you win title after title?
At Celtic, you have to win. It doesn't matter if Barcelona, Manchester United or Manchester City came to town tomorrow. The fans expect you to win.
"You have to realise, if you finish second, you fail. The new chief executive needs to look at the bigger picture. You have to get trophies back and get the pendulum swinging back your way.
"Nine years of dominance... they have to get that back. If he thinks he will get one or two years of grace, he won't get it. And rightly so, he shouldn't get it.
"That's the nature of Celtic. It's a worldwide club. Not just European. It's worldwide with the fanbase. He has to realise he must hit the ground running."
Former Bournemouth boss Eddie Howe, who led the club from the pit of League Two to the Premier League, as well as ex-Chelsea head coach Frank Lampard and current Scotland boss Steve Clarke have all been linked with the Celtic manager's job.
Lambert, who ruled himself out of the running to replace Lennon, says it "doesn't matter" who the club bring in, instead feeling that whoever it is must understand the pressure that comes with the role.
"It doesn't matter who the next Celtic manager is," he added. "Whether it's a foreign manager or a British guy, you're hoping whoever goes in there understands how to win every week. Not to finish second. Not to be runners-up in cup finals.
"The criticism would come heavily, and so it should. That's the way it should be. You should have the pressure on your shoulders at Celtic. If you are a player there, it is a responsibility.
"It's a worldwide club. It's not a small club where you might get away with losing three and drawing two. You have to win every single week. That's on whoever comes in."
Asked if he would consider applying for the Celtic job, given his connection with the club as a former player and fan, Ipswich boss Lambert said: "I played for eight years, but I left the Glasgow scene a long time ago.
"That's not my life anymore. I don't want to tarnish the good feelings I have with the Celtic fans. We won a hell of a lot, stopping Rangers win ten [league titles] in a row in 1998. That was an incredible achievement.
"Maybe I'll go back as a fan, that's all I can say."
Celtic are back live on Sky Sports on March 7 when they travel to Tannadice to take on Dundee United.
'Eddie Howe could develop young Celtic players'
Former Celtic striker Scott McDonald feels Eddie Howe could help develop Celtic's younger players if he was to take the job, but also feels Belgium boss Roberto Martinez could be a strong choice.
"I think he's someone that Celtic will look at seriously," McDonald said of Howe, who was voted English Football League Manager of the Decade in 2015.
"He's the type of manager who will want to develop younger players, and bring in younger players who the club could then sell on for more money. Celtic are always looking to do that within their business model.
"For me, the No 1 choice would be Roberto Martinez along with [Belgium's Scottish coach] Shaun Maloney. Roberto played in Scotland, he understands it up here, and obviously Shaun totally gets it."
Fans of Scottish football can now catch up on all the latest news and talking points via our weekly podcast featuring analysis from Kris Boyd and Andy Walker.