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.
Former striker Asad, who helped Velez Sarsfield win the South American and world club titles in 1994, said he told club president Carlos Abdo he wanted to continue in charge of San Lorenzo but was told he had to go.
The table that really matters now for the Saints, who according to media reports have a debt of more than 150 million Argentine pesos ($35 million), is the parallel relegation standings where they are in the bottom four.
Relegation is calculated on points averages over three campaigns and, as things stand, San Lorenzo will need a play-off against a Nacional B side at the end of the season in June to try to retain their top-flight status.
ANGRY FANS
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.
The home match against All Boys that weekend was postponed and played nine days ago.
San Lorenzo lost the game and Bottinelli had the misfortune to score an own goal that gave All Boys a 1-0 victory.
Asad is the sixth coach to leave his job in the Apertura championship, the first of two in the Argentine season.
