McCarthy, 25, joined Everton in September 2013 and played more than 30 games in all competitions for the club last season, but Sissoko's arrival could have put the Ireland international's place in manager Ronald Koeman's squad under threat.
"Sissoko is a great player. 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," Moshiri told British media.
"Keeping James McCarthy was a priority and ultimately we could not proceed with a deal that would jeopardise his place at Everton. We wish Sissoko the best."
Everton have picked up seven points from the opening three games and will look to continue their impressive start to the season when they face Sunderland at the Stadium of Light on Sept. 12.
(Reporting by Ian Rodricks in Bengaluru)
