The French club is disappointed with the departure on a season-long loan of its star player, but claims it had no other option but to allow him to leave.
The prolific attacker joined Monaco from Atletico Madrid in the summer of 2013, but his impact was limited in his first season at the Stade Louis II side due to a serious knee injury sustained in January.
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Irrespective of his recent fitness woes, Falcao was consistently linked with a move away from Monaco this summer and eventually signed a one-year loan deal with United on Monday, with the Premier League club retaining the option to buy the star at the end of his short-term contract.
"I regret Falcao's departure, particularly for our fans," Vasilyev told reporters. "However, we felt that from the moment the player had expressed his desire to join Manchester United, it would have been wrong to block his transfer."
The 28-year-old, who missed this summer's World Cup in Brazil due to his knee injury, netted 11 goals in 20 Ligue 1 appearances for Monaco in 2013-14.