Born in Valladolid, Castile and León, Falagán played in the lower leagues until 1993, when he represented Hércules CF in Segunda División loaned by neighbouring Valencia CF.
In 1995–96, Falagán played all 42 matches in La Liga with SD Compostela, his solid performances earning him a place in Javier Clemente's shortlist for UEFA Euro 1996 as one of the five goalkeepers.
[1] In the following season he appeared significantly less, but still managed to be the most used player in his position as the Galicians again retained their league status.
[2] Falagán played three more seasons in the second level, with Hércules and CP Mérida.
[4] He then continued coaching goalkeepers at Chinese club Guangzhou Evergrande.