Abramovich, who's been Blues owner since 2003, made the announcement amid Russia's invasion of Ukraine.
The statement suggests he will no longer make key decisions in the running of the club, however, Neville hugely doubts whether these will be left to the chosen six.
Neville also urged the Russian oligarch to make his position on the invasion of Ukraine clear.
"Maybe myself and most others who saw that statement thought this sounded like a noble gesture, the right thing to do," Neville told Sky Sports.
"But when you look at who the charity trustees are - Emma Hayes, the Chelsea Women's manager, Piara Power who set up Kick It Out, John Devine… it's quite clear that they're not going to be running Chelsea Football Club.
"One of the smartest things that I think Roman Abramovich has done over the last 20 years is not speak, not make statements.
"The statement that he's made left more questions than answers. If anything, I thought it was a cowardly approach to throw a hospital pass to the good people on the charitable and foundation board.
"It's quite clear he runs the club with Marina Granovskaia and Petr Cech on the football side.
"These owners of the top six clubs are insulated from reality. They think they can put a smart PR team around them and con us with fancy work but unfortunately it doesn't work.
"There's no way that the charitable foundation of Chelsea are running the club and I'm not sure why Roman Abramovich made that statement.
"If he wanted to make a statement of any note, it would have been whether he supports the war in Ukraine or if he opposes it."
Commenting on Abramovich's statement, Tuchel said: "Absolutely it includes him and this reflects my opinion and everyone else's in the club.
"No, we haven't [had communication] but that's not unusual because I've had daily conversations with Petr Cech and very regular conversations with Marina, who are both in charge of football. It's my understanding that they will stay in charge, that will not change a lot for me.
"It was difficult and it was a distraction because we are aware, we are watching news and people are aware and we're a bit shocked at the situation in Ukraine.
"This was more of less it, but at the end - approaching this final - I allowed us to be sportsmen and football players and to focus on this match of football and to a certain degree to enjoy it because we know there are much, much more important things out there than football.
"And still we are here to play a match and this is what the players and spectators deserve."