The midfielder believes his side's poor finishing was their downfall in Sunday's contest
The midfielder had given the visitors an early lead after heading home Carlos Sanchez's whipped cross before Boca's Santiago Silva restored parity.
Speaking to reporters after the game, Lanzini stated that poor finishing cost River the chance to secure the bragging rights and, more importantly, the opportunity to climb to within two points of Lanus at the summit of the Primera Division.
"We will leave with a bitter taste in our mouth. We came for the three points. We knew it would be difficult but we had several opportunities to score. I think we just lacked the coolness in front of goal," he said.
"We needed to win, but we have to move on and think about our next game."
The referee was forced to temporarily halt proceedings a number of times throughout the game due to incidents involving flares and fireworks and Boca goalkeeper, Agustin Orion, believes the stoppages disrupted the game's fluency.
"On the field we had a lot of possession, but there were so many interruptions."