Falcao, who plays his club football for French Ligue 1 side Monaco, was seen in discussion with Peruvian players with his hand covering his mouth towards the end of the 1-1 draw in Lima.
Several South American media have published photos of the moment and dubbed it the ‘Lima Pact’.
With the scores at 1-1, Colombia were set to qualify automatically for the finals in Russia while Peru were heading for a play-off against New Zealand.
“In the last five minutes, the Colombians approached us. They knew what the situation was in the other games,” Tapia told Panamericana TV station in an interview aired on Wednesday.
“So we managed the game as we needed to… I spoke with Radamel, who told me we were both qualified (as things stood), but it’s football and we play to win.”
Asked by Colombian media in the mixed zone after the match what he’d said to Peru’s captain Paolo Guerrero, Falcao said: “We knew what was happening in the other matches, we were playing with (the knowledge of) the other results and in that moment (I tried) to transmit that (to Peru).”
One of Peru’s coaching staff, Nolberto Solano, the former Newcastle United winger, dismissed any notion of a pact between the teams.
“We needed to win, them too. What pact? That’s speculation,” he told RPP radio station.
“Obviously, at the end, we knew what the other results were and you tell yourself: ‘calm it down a bit, we mustn’t take any risks’.”
At the end of the game, both sides played keep ball without showing any desire to attack.