River coach Ramon Diaz apologised for his team's display after they found themselves 4-1 down after only half an hour in Sunday night's match.
"We didn't want our challenge to finish like this," Diaz told reporters after his side dropped six points behind leaders Newell's Old Boys with one match to play.
"I apologise to our supporters for the way we played today. Lanus were ruthless for the whole 90 minutes."
Lanus are also six points behind leaders Newell's Old Boys, who beat Atletico Rafaela 3-0, and need an unlikely combination of results to force a play off.
On Wednesday, they play the remaining 45 minutes of their match away to Estudiantes which was called off at half-time last week after a fan was killed in clashes outside the stadium.
They will have to overturn a 2-0 half-time deficit in that game, then beat San Lorenzo in their final match and hope that Newell's lose to Argentinos Juniors.
If Newell's and Lanus finish level on points, an extra match will take place between the two.