The German was sent off at full-time alongside counterpart Antonio Conte after the two men squared off following a tasty handshake.
Tuchel and Conte were both booked during the match in a major dugout melee after Pierre-Emile Hojbjerg's goal, with Chelsea incensed that Kai Havertz was not awarded a free-kick in the build-up.
Harry Kane buried an added-time header to snatch a draw, after Christian Romero had avoided any censure for pulling Marc Cucurella's hair.
A VAR check ruled out a red card for Romero's hair pull, but Chelsea were not even awarded a free-kick. And from the next corner, Kane headed in to steal the draw.
Chelsea fans have long claimed an agenda from Taylor against the Blues, and Tuchel knew full well he would draw the wrath of the FA upon himself with his comments in response.
Asked if he thinks Taylor should not referee Chelsea again, Tuchel replied: "Maybe it would be better, maybe it would be better.
"But honestly we also have VAR, to help make the right decisions.
"Since when can players have their hair pulled, since when is that?
"And if he does not see it, I don't blame him - I didn't see it.
"But we have people at VAR who check this, and then you see it. And then what?
"And how can this not be a free-kick, and then a red card? How?
"This does not even have to do with the referee in this case.
"If he does not see something that's why we have people to check if this is a decisive error or not."
When asked again about Chelsea supporters' concerns about Taylor's officiating, Tuchel continued: "I don't think that just some of the fans think that: I can assure you that the whole dressing room of us, every person thinks that.
"Not only the fans. You know the players, they know what's going on when they are on the pitch. They know it."
Asked if the players are worried when Taylor is in charge, Tuchel added: "Yeah, of course."