Former international Laurence Docherty led the complaints after English hockey's Players' Player of the Year Alan Forsyth - a Scot - was left out.
"This is the most outrageous situation I have heard of," Docherty said.
But GB Hockey responded that squad selection was "based on performance criteria only, not on nationality".
It added: "Selection is exceptionally difficult and every decision is taken with due diligence and in the best interests of Great Britain Hockey."
Scot Docherty himself switched allegiance to the Netherlands after being left out of the Great Britain squad for Sydney 2000.
Docherty believes Forsyth - who was also the top scorer in England's top league in 2014-15 - is just one of the Scots who deserved a place in the men's or women's squads.
The 23-year-old was recently capped by Great Britain at the World League Finals in India.
"Twenty-plus goals and not selected - mental," Docherty added.
In a statement, Scottish Hockey expressed its disappointment, saying: "Our athletes have worked exceptionally hard, made significant personal and professional sacrifices and shown a fantastic commitment to competing in a sport they love.
"We are disappointed for them that they have not been rewarded for their efforts. They are a credit to Scottish Hockey and the sport."
Great Britain Hockey has defended its Olympic squad selection, after it was criticised for an absence of Scottish players.