Moyes got his first experience of Manchester United's global appeal in Bangkok as fans turned out in force to welcome their arrival in Thailand at the start of a five-match summer tour.
Even more can be guaranteed at Friday's open training session ahead of Saturday's meeting with the Singha All Stars, which marks the first game of Moyes' reign.
Yet it is not until the Red Devils start the season with a run of five successive live Premier League TV games in the middle of next month that the real assessment of the Scot's work can begin and Cole knows Ferguson's shadow will loom large.
"It is a massive act for David Moyes to follow," said Cole.
"You are losing the most successful manager in English football history.
"The new manager comes in and everyone says to themselves 'we have a chance now'. That is how I would see it anyway.
"Sir Alex Ferguson is the Godfather of football. When you have a presence like he had, it guarantees you a certain amount of points every season.
"Some people just know how to get that little bit more. Sir Alex Ferguson could turn a minute of injury-time into 90 seconds.
"What he said at half-time, full-time or in the media meant something might go his way the following week."
- Sports & Recreation
- David Moyes
- Manchester United
- Sir Alex Ferguson