Torres, 24, was sent off late in the game for pushing a ball boy after he allegedly racially abused him.
The Ecuador international cried after the encounter and later revealed the alleged incident.
"What happened today cannot continue to happen," Torres said. "I was sent off for words that hurt too much.
"It's affected me and I'm sad. My teammates are not bothered by the colour of my skin, they like me as I am. They know the person I am and the pain that I'm going through right now."
Santos Laguna captain Matheus Doria called for an investigation to be carried out.
"This can't happen anywhere, please review the video images, there were racist acts," Doria said. "We are all the same, this [racism] is something of the past, it's old. We are here to do our job and those on the outside cannot do this."
Later on Friday, Santos issued the following statement regarding the incident: "Our player Felix Torres received discriminatory and racist insults from members of the rival team, acts that we condemn and categorically reject.
"What happened caused significant harm to our player, our institution, Liga MX and our industry. We hope that the Liga BBVA MX and the Federacion Mexicana de Futbol (Mexican football federation) carry out a full and far-reaching investigation into the events; that these types of events do not happen again and are eradicated from our game.
"Felix has our full support and we will do whatever required to help him through this difficult time."
Alejandro Irarragorri, president of Grupo Otegi, that owns Santos Laguna, condemned the alleged incident and wrote: "NO TO RACISM, to walk into the changing room and see a player crying because of the insults he has received is terrible."
Atletico San Luis assistant coach Pedro Garcia also expressed his disgust after the game and said: "We come to play, not to discriminate or attack. We don't have that ideology."