The deal was signed last week by President Juan Manuel Santos and Farc leader Timoleon Jimenez after nearly four years of negotiations.
But it needed to be ratified by Colombians in order to come into force.
Addressing the nation, President Santos said he accepted the result but would continue working to achieve peace.
He said the current ceasefire remained in place and that he had ordered negotiators to travel to Cuba to consult Farc leaders on the next move.
"I won't give up," he said. "I'll continue the search for peace until the last moment of my mandate because that's the way to leave a better country to our children."
Meanwhile the Farc leader, known as Timochenko, said the group remained committed to securing an end to the war.
He also criticised the No campaign.