The Toffees looked set to sign Sissoko in the final hours of the summer transfer window before Tottenham entered the race, matching their bid at the eleventh hour.
The Spurs offer of £30million - to be paid in five instalments of £6m across the five years of Sissoko's new deal - reportedly spun the transfer in favour of the north London club at Everton's expense.
"Sissoko is a great player," Moshiri said in a statement to Sky Sports' Jim White. "But when I bought into Everton, I made it clear I was proud to join a family. And we don't turn our backs on our own.