The winger was given his marching orders for grabbing Sterling by the neck, twice, in retaliation to a late tackle from the Liverpool man.
Both players were sent off for the incident but it was Valencia's overzealous reaction that was widely criticised.
Valencia said the injury suffered by team-mate Segundo Castillo in a friendly against Mexico on Saturday – which nearly forced him to withdraw from the FIFA World Cup – played a role in his actions.
"I apologised to the team after the match and the coach (Reinaldo Rueda)," Valencia said afterwards.
"I am sorry for the fight with Sterling. When he tackled me I thought about Segundo Castillo.
"He nearly missed the World Cup because of injury and I feared I would too but thankfully I am okay."
In an entertaining friendly in Miami, Ecuador needed a stunning 70th-minute equaliser from Michael Arroyo to claim a share of the spoils.
The red cards given to Valencia and Sterling will have no impact on the World Cup, which Ecuador open with a clash against Switzerland on June 15.
