UCLA men's soccer had the opportunity to play against the likes of Jozy Altidore and Clint Dempsey.
Edwards Jr. was selected by Orlando City SC and Simmons was selected by the Philadelphia Union.
Senior midfielder Leo Stolz was selected 18th overall by the New York Red Bulls on Thursday.
Stolz earned his second Player of the Year award for the 2014 season on Tuesday.
Leo Stolz is the third UCLA Men's Soccer player to earn the National Player of the Year award.
Abu Danladi (First), Seyi Adekoya (Second) & Chase Gasper (Second) were all selected.
Adekoya, Danladi and Gasper joined Amick and Stolz in earning postseason awards.
Freshman striker Abu Danladi posted five goals and six assists this season for the Bruins.
Junior forward scored two goals in the semifinals to lead UCLA to the championship game.
Leo Stolz was named to the first team and Michael Amick was named to the third team.
UCLA lost to Virginia 0-0 (4-2 PKs) in the College Cup Finals on Sunday afternoon.
UCLA takes on Virginia at 9:00am PT on December 14 in the NCAA Championship game.