Tuchel ruthlessly took off the English forward just 30 minutes after coming on against Southampton on Saturday, before publicly slamming his performance.
Poyet - who won four major trophies during his spell at Stamford Bridge - has stated Tuchel can get away with what he did as he's just arrived in England.
Speaking on Monday Night Football, the 53-year-old said: "I think if this was done by Frank Lampard today, he would be killed in the press by every single reporter.
“But because he's (Tuchel) new, and because he's just arrived and he's doing well, it's just normal.
"When you go to a new club, in the first few weeks everything is alright, even if you make a mistake.
“If you make the same mistake one year later and you're in the same position you get the sack, that's natural."