The Gabon international was at the centre of a host of disciplinary issues before making his big-money move to Arsenal in January.
Speaking about the situation, Dortmund chief said he has offered an ultimatum to his team: "On Thursday, I laid it on the line for the squad, the next player who does something like [Aubameyang] will fail miserably. He'll run into major problems".
"The next player who tries to put us under pressure by withholding performances or even going on strike will not get a pass and will instead sit in the stands".
He concluded: "They are all aware of it. This is now a public statement. Follow Dembele and Aubameyang, there is now an overriding interest for the club, we need to get a better structure into our squad again".
Watzke also gave his opinion on why Aubameyang left: "[He left] because we had the impression there will be no new start for him in the second-half of the season. Not with the fans, not with the team. Too much had been damaged through his behavious".
The 28-year-old won't take too much offence to the words of his former director after netting on his full debut for Arsenal in their 5-1 thrashing of Everton on Saturday.