Desailly believes 33-year-old Villas-Boas cannot afford to make any mistakes if he is to gain the respect from the Blues' star studded squad.
Failure to do so, and the former Porto manager could face a player backlash similar to the one that plagued Roy Hodgson during his short-lived spell at Liverpool last season.
"All the pressure is on the shoulders of the coach. It's all up to him. The next step is to get the consideration of the players," Desailly said while attending the Barclays Asia Trophy tour in Hong Kong.
"If I was in the squad like this, with a young coach like this with not too much experience, who has had one win with Porto, it could be a little problem.
"The Chelsea players are really established players. If I was there, a World Cup winner, I would be expecting the coach to show me during the training sessions, and in his substitutions and tactics, how clear he is in his vision.
"If he makes any mistakes, then you will see that they will not follow him. Subconsciously - not necessarily on purpose - they will be thinking that the guy who is supposed to be managing is not on their level. He has to be clever on how he manages his team.
"This is the challenge for the manager. It's a big consideration for me, given the young age that he is.
"His first few weeks could be vital. It's vital in that, if they don't perform - like Liverpool last year early in the season - the players and their consideration will change. The manager needs the players to follow him, to follow his vision.
"If Manchester United get a bad result at the beginning of the season they remain calm, even though the media is very hot on them. The players stay with the programme, with the training sessions, and they stay confident.
"They come back slowly and it comes good. But Chelsea will face problems if the players don't follow his vision and be less confident."
One of the main challenges Villas-Boas will face next season will be getting the best out of Chelsea's £50million striker Fernando Torres. The Spaniard has failed to live up to his hefty price tag since moving from Liverpool in the January transfer window and the striker's pre-season form has already brought the new manager some tricky moments at recent press conferences.
Not one to shy away from opinion, Desailly claims Villas-Boas needs to do more to boost the confidence of the team.
"I've seen him [Andre] in the press conference and I could feel he was already annoyed. He is the guy with the vision and ambition," Desailly said.
"Come on, you are the man - show us. He should be talking up the players, saying: ‘Come on.'
"The main challenge for Villas-Boas is Torres: How to get him back to his best physically, but also finding the players around him that allow him to express himself. He needs to be clever and find something extra.
"Torres is a confirmed top-class player, but is in the same sort of moment as when Shevchenko went to Chelsea, even if he is younger. Shevchenko was a top class player, but physically not at the top level.
"The team weren't helping him too much and didn't give him the ball. It's the same for Torres. He's not getting the ball soon enough.
"Lampard is a great player and a friend of mine, but he does not give you the ball straight away. He keeps the ball, then gives it to someone else to get it back and score [himself]. He's not somebody who gets the team to play.
"Torres needs the ball early, which is why it's not working.
"Torres' problem is a combination of the physical and mental. At first, you're a little bit down physically and realise you're not capable of the same sort of effort you were before. Then you lose your confidence and it becomes at mental issue.
"At Atletico Madrid, he looked like a killer. Even three years ago at Liverpool he reminded me of Marco van Basten. If he'd have maintained that level he had the biggest potential of anyone in European football.
"He was the complete player. He could head the ball, left foot, right foot, speed, great first touch. He was like Van Basten. That's why he's the key.
"But it will come. The guy is 27, the talent is still there and he's not scared about the Premier League, he doesn't need to adapt to the speed or skill of the Premier League or commitment. He still has the pace."
Earlier in the week, Chelsea breezed into the final of the Barclays Asia Trophy with a comfortable 4-0 win over Kitchee at Hong Kong Stadium.
The Blues play Aston Villa in the final on Saturday.