Escobar, brother of the late Colombia international Andres Escobar who was murdered 10 days after scoring an own goal at the 1994 World Cup, was scathing about men he has criticised repeatedly over the last few months for lack of effort.
"The directors gave me their support and signed four players who didn't perform and the responsibility is mine," he told El Tiempo newspaper.
"There are players who are only interested in getting a good contract but don't respond to the team's obligations and the directors have their hands tied until their contracts end," he added.
"FIFA should change this ruling."
"Unfortunately, the players in our game need to be more sincere. If this doesn't change, it could be fatal for our football."
Escobar took over last July and led his team to the runners-up spot in the Clausura championship played in the second half of last season. His team qualified for this year's Libertadores Cup but were eliminated in the group stage.
Former Colombia midfielder Leonel Alvarez, who played alongside Andres Escobar in 1994, was named as his replacement, Medellin said on their website.
In other coaching moves, Medellin's local rivals Atletico Nacional named Argentine Ramon Cabrera as their third coach of the year while Pedro Sarmiento said he was quitting Pereira.
America coach Diego Umana, who had been tipped to take over at Bogota club Santa Fe, said he would be staying with the Red Devils, where he won the Clausura championship last year.
Umana, who once said he contemplated suicide after his team missed out on the Clausura final in 2007 and received death threats when he was coach at Deportes Quindio in 2006, said the fans were behind his decision.
"I'm going to stay where the public like me," Umana, who also suffered from heart problems at Quindio, told the website Futbolred.com
