Striker Llorente has turned down the offer of a contract extension beyond next season and has been linked in the media with moves to England and Italy, while Bayern Munich have made clear their interest in signing versatile midfielder Martinez.
"I choose the squads taking into account such things as form and state of mind that will benefit the team and have decided to leave them out," Argentine coach Marcelo Bielsa told a news conference on Saturday.
Bilbao fans whistled and jeered at the two players in training during the week and they were not present at the Saturday session.
"It is a difficult situation because all the positions are understandable," Bielsa added.
"Martinez and Llorente are within their rights, it is fair for the club to want a particular style and philosophy and I understand the fans, even if I don't share their way of expressing themselves.
"Bayern know what they are doing at every step. They are an example of how to go about doing these things. If we get money in, I won't be demanding new signings."
Martinez, 23, and Llorente, 27, were members of Spain's victorious Euro 2012 squad and were central figures for Bilbao last season as the club reached the finals of the Europa League and Copa del Rey.