The Black Cats boss was speaking frankly about the unique challenges that the January transfer market presents and used Colombian superstar's to highlight his point.
Poyet told the Sunderland Echo: “Some people say to me ‘maybe you can get a player on loan who changes your season’.
“Where is that player?
“Unless it’s someone coming from a bad injury and needs to play, it’s difficult.
“Now if Man United want us to take Falcao for six months... We will do.
“But that doesn’t happen a lot.
“You need to be very smart in January.”
Sunderland have scored just 13 goals in the league this season and while reinforcements in the striker's department are a priorirty, Poyet's words will come as a warning to the Sunderland faithful not to expect miracles when the transfer window re-opens on January 1.
Despite only winning two matches in the English Premiership this season, the Black Cats find themselves in 14th position on the table.
Poyet's side host West Ham United at the Stadium of Light on Saturday.
The match kicks off at 17:00.