The Italian has been linked with his nation’s national team job this week.
“Every year after Chelsea win the league something changes,” Poyet told BetStars.
“They’ve had a lot of successful managers but for whatever reason the year after (they win the league) they’ve been quite difficult to manage.
“I think it was a difficult summer for Chelsea. The idea of being champions and one simple thing like changing your striker influenced the team in an incredible way.
“We don’t know what happened with Diego Costa, Conte and everyone. There were decisions made and when you’re at a club like Chelsea, you’re looking for certain special players and there are a few who are still adapting and trying to get into the system.
“If I remember last season, Chelsea had a spell when they weren’t doing so well and then they changed the system and went to five at the back and they became really strong and found the balance to both defend well and create plenty of chances.
“I think this year there is not a clear first XI at Chelsea and they have paid the price for that, especially playing so many games in both the Champions League and Premier League.
“I hope so for many reasons it is different this time. You want to prevent a situation like with Jose Mourinho, winning the league twice and then leaving, as he did in his second spell.
“Ancelotti winning the league and then leaving, Roberto Di Matteo winning the Champions League and then leaving, but it looks like the opposite at the moment – it’s better not to win as you can stay longer! Every club works in a different manner and Chelsea is a special club.”