The Monaco striker said he tried to make it clear to Peru's players late in the Lima clash that, with Chile losing to Brazil, a draw would be enough to send Colombia through automatically and secure the hosts a play-off spot.
The two nations played out a 1-1 draw in their final qualifier this week, which earned the Colombians their place at the Russian Federation showpiece while Peru are through to the playoffs, ahead of Chile on goal difference.
Jose Pekerman singled out debutant Duvan Zapata after Colombia earned a 1-1 draw with Peru to qualify for the World Cup on Tuesday.
Colombia and Peru's alleged pact must have infuriated Chile, who were heading for Russian Federation until Peru's 76th minute equaliser. With Chile falling to Brazil 3-0, Peru chose to play safe, taking no chances and running out the clock in extra time.
Federation Internationale de Football Association are yet to make any comment regarding the accusations of match-fixing.
After Falcao's message was passed around the team, the Peru players played out the final minute of the match passing the ball around the defence before the referee blew the final whistle. "They knew what the situation was in the other games", Tapia told Panamericana TV. "With Duvan in his first game, we need him with his power", Pekerman said post-match.
One of Peru's coaching staff, Nolberto Solano, the former Newcastle United winger, dismissed any notion of a pact between the teams.
At the end of a thrilling, unpredictable South American qualifying campaign, Colombia are in the World Cup and Peru are two games away from joining them.