A move for the 25-year-old Balogun fell through after he changed his mind following a medical at Everton's Finch Farm training base.
The United States international had emerged as a late target after Guinea-Bissau striker Beto completed a permanent switch to Serie A club Fiorentina.
Everton also explored deals for Manchester United forward Joshua Zirkzee and Aston Villa frontman Tammy Abraham but were unable to convince either to join.
The Toffees did sign Jack Grealish on a season-long loan deal from Manchester City, but lost star attacker Iliman Ndiaye to City in a deal worth £65m.
Moyes said: "I am disappointed that we didn't do more business and things didn't go our way in the end."
Everton will now focus on the upcoming season with a squad that has undergone significant changes.