After an impressive season-long loan at Sunderland last season, the club desperately tried to sign the Liverpool man on a permanent deal, but they were ultimately unsuccessful.
Despite both Sunderland and Harry Redknapp's QPR having bids of £14 million accepted, neither club was able to convince the Italian forward to sign on the dotted line.
Now the Black Cats boss has jumped to defend Borini by claiming he would have snubbed a move away too.
Poyet said: "His aim was Liverpool first and then any team playing in Europe next.
"Now it is very easy to say our move was a little bit too early because all the time he was trying to wait for one of the top teams, but back then we were in a rush to get the player.
"I thought we had a great chance but in the end we couldn't get him. I understand his point of view. I can put myself in his point of view and I would like to be honest and say maybe I would have done the same if I was him."
The Uruguayan would not rule out trying to sign the 23-year-old again in January, and added that loan signing Ricky Alvarez from Inter Milan is not a replacement for Borini.
"Could we revisit in January? It depends on where we are -- I wouldn't like to say yes or no because I don't know how we are going to be or how he is going to be.
"People will think Ricky is the substitute for Borini, but for me he is not. Ricky is a player who is exciting on the ball and will create things on his own, but he's not a top scorer."
With Daniel Sturridge being ruled out for three-weeks with injury, Borini might actually end up closer to the Liverpool first-team than many had expected. They play seven games in the next three weeks and have only Borini, Balotelli and Lambert as their available strikers, so you would imagine there will be a little bit of rotation up top.