Despite their fifth-place position in the current championship, River dropped into a relegation zone based on their average points over the last three seasons.
River were leading San Lorenzo at the Monumental when Carrizo let a head-height shot from 25 metres by Jonathan Ferrari slip though his fingers and drop into the net in the 73rd minute for a 1-1 draw.
"A mistake by me and I gave away the triumph," Carrizo, whose errors also contributed to River's defeat by arch-rivals Boca Juniors last weekend, told reporters.
Striker Leandro Caruso had given River the lead with a neat back-heel close to the half-hour mark.
River hold an Argentine record 33 league titles and have never been relegated but will face a promotion playoff with a second-tier Nacional B side if their three-season points average does not improve.
They have traded places with Olimpo, who beat Argentinos Juniors 1-0 on Saturday and whom River visit next weekend.
MATCH ABANDONED
The relegation heat also intensified at Huracan, whose fans rioted with their team 2-0 down at home to title holders Estudiantes forcing the referee to abandon the match with an hour still to play on Saturday.
Home fans began throwing seats, stones and other objects onto the pitch from the stands after their team conceded the second goal.
After Estudiantes fans taunted the Huracan supporters with relegation chants and joined in the fighting, referee German Delfino abandoned the match and the Argentine Football Association is expected to rule on the issue on Thursday.
Financially troubled Independiente, like River one of Argentina's "Big Five" who had slipped dangerously close to the relegation zone, eased their worries by beating Colon 3-1 after the players were persuaded not to strike over unpaid wages.
Title favourites Velez Sarsfield are three points clear with four matches to go after Sunday's 2-0 home win over Gimnasia.
However, second-placed Godoy Cruz could have been only one point behind Velez. They drew 1-1 at Banfield on Friday in a match they should have won.
A long-range strike from Diego Villar came down off the bar almost half a metre inside the goal but was ruled not to have crossed the line.
Embarrassed referee Saul Laverni admitted on Saturday after seeing video replays that Villar's goal should have stood.
"I can't hide under the carpet what everyone saw nor justify the unjustifiable," he said. "I did not have a good night."
Lanus kept pace with the front two when they beat Tigre 3-0 away with a hat-trick by Silvio Romero.
