The Saints lost 1-0 to promoted Union on Sunday, their fifth defeat in eight home games in the Apertura championship.
San Lorenzo are 15th in the 20-team table with 15 points from as many matches and have taken one point from their last four games.
"I came here with a lot of hope, it didn't work out. This is going to be a thorn in my side," Asad told a news conference on Monday.
"I'm calm because I tried and we worked hard but we never managed to get it right," added the 40-year-old who joined from Ecuador's Emelec five months ago after cutting his coaching teeth at Argentine side Godoy Cruz.
In this sense they are in a similar position to River Plate last June when the 'Millionaires' lost a play-off and were relegated amid scenes of violence from fans at their Monumental stadium.
San Lorenzo supporters have been angry with their team for weeks, their demands for more commitment turning into a chorus of "Go, all of you" encompassing coach, players and directors.
One 'barra brava' hooligan fan attacked central defender Jonathan Bottinelli three weeks ago after a training session.
