Mitja Blazic and Niki Kern called the ceremony "humiliating".
Slovenia's Parliament in July passed legislation recognising the rights of same-sex couples. It went into effect on Friday.
The law lets gay and lesbian couples register their unions and give partners access to each others' pensions and property.
But, a stipulation in the law bars couples from having guests at the registry ceremony. Only the couple and the registrant can be present.
Blazic and Kern signed the registry at a municipal registration office in a state building. When they came out they told friends and reporters the affair was cold and without feeling.
"It looked more like a car registration, not a wedding ceremony," Blazic said.
The couple complained that heterosexual couples are allowed to marry, can have family and friends attend and are able to celebrate. "It's discrimination," said Blazic.
Under the law same-sex partners must register 30 days in advance and submit documents proving they are sane, in good health and not already married.
LGBT rights groups said the law was only a small step in the right direction. The groups said they hoped the government would enact full marriage rights.