The Sunderland boss was assistant manager at Leeds when the winger was loaned to the Yorkshire side.
Johnson, then of Middlesbrough, was loaned to Leeds when Poyet was Dennis Wise's assistant at Elland Road.
But the now Sunderland winger was soon sent back to the Riverside - because he simply didn't suit Wise's style of play.
“He was very, very young when he was with us at Leeds. After a while Dennis sent him back," the Sunderland manager is quoted as saying by the Chronicle.
“He had ability then, he was very young, the team was in a terrible situation, the game Wisey wanted to play did not really suit Adam so it was a bit of a problem.”
In praise of Leeds, Sunderland boss Poyet added: “Sometimes I wonder why one of these incredible wealthy people does not buy Leeds.
“It will be good for English football if they come back to the Premier League, though. I am 100 per cent sure of that.”