The West Africans held their own for 74 minutes before being stung by a Yerry Mina header, which earned Los Cafeteros a 1-0 triumph at Samara's Cosmos Arena in Russia.
The defeat has sent the Teranga Lions, who needed just a draw from the game to make the round of 16, out of the tournament.
"Senegal were a very worthy team, very strong," Falcao said.
"They wanted to win the game but we finally settled in better and got the winning goal.
"Senegal pitifully stays out but I think they did everything to qualify.
"They were very physical, played on the counter and made it complicated for us in the first half.
"Our team was strong, showed character and in the end took the three points against a great team."
Ultimately, Colombia, who sat third on the table before matchday three, topped Group H by the turn of events.
"The three group games were very positive although we lost to Japan," Falcao remarked.
"What happened there gave me hope for what was coming with Poland and Senegal."
Los Cafeteros, who played at the World Cup for the first time in 1962, are hoping to better their quarter-final berth achieved in Brazil four years ago. It remains their best ever finish at the tournament.
Russia 2018 marks their sixth appearance at the global showpiece.