Boca lost 3-1 in extra time in last Sunday's second leg in Madrid to make it 5-3 on aggregate, BBC Sport reported.
The game had been postponed and then relocated after River fans attacked the Boca bus and injured players before their second leg in Buenos Aires.
Former Boca striker Schelotto had been in charge for two and a half years.
The club has won the Argentine title for the past two seasons and currently sits sixth.
"Beyond the pain of not having won the cup, I'm going with peace of mind of having given everything," the former Argentina international said.
Club president Daniel Angelici added, "Though the pain and sadness have not yet gone, we understand that the best thing for Boca is a change, to start the year with a new coach."
His reign ended with one of the biggest games in South American football history – as Buenos Aires' big rivals met in the continent's version of the Champions League final for the first time.
The first leg – Boca's home game – ended 2-2, but the second meeting was postponed when Boca's bus was attacked by River fans on its way to the stadium. Boca players suffered cuts from broken windows and were also affected by the tear gas used by police to disperse the crowds.
By contrast, River Plate coach Marcelo Gallardo pledged his future to the club earlier this week, having been linked to European clubs.
River plays in this month's FIFA Club World Cup as a result of its win.