Benstiti told the French publication Le Progres that Rapinoe will not be part of the Reign roster for the tournament.
Her absence leaves the NWSL without one of its biggest stars as it attempts to become the first team sports league in the United States to resume games.
"It's a shame," Benstiti told Le Progres. "I understand her motivations but I'm disappointed and frustrated that she won't be with us to take part in the tournament. Megan is important for the group and we would've been able to create something really important with the club if she joined the group.
"The team and women's football are going to miss her a lot."
The NWSL announced at the end of May that it will return to competition with the monthlong tournament in Utah. All games will be played in the Salt Lake City area, with players and staff housed in what the league described as a self-contained "village" of hotels and apartments near the facilities.
The league stressed that the decision whether to participate is each individual player's, and those who do not participate will be paid their full salaries. U.S. Soccer also confirmed the same was true for national team players whose NWSL salaries are paid directly by the federation.
While most coaches and owners who have spoken publicly have expressed full support for players, Benstiti's comments are among the first to express any displeasure with a player electing not to participate. Benstiti is in his first year as OL Reign coach after taking over for new U.S. women's national team coach Vlatko Andonovski. He previously coached in Europe, most notably with Lyon and Paris Saint-Germain.
Reign CEO Bill Predmore said last week that the organization would try to answer any questions players had about the tournament setup.
"Every player has a choice to make for herself; we're not forcing a timeline on that," Predmore said. "If for whatever reason they're not comfortable, we'll be supportive of their decision."
In addition to concerns about the coronavirus, almost all of the tournament's games will be played on artificial turf. A team could play as many as seven games in the span of a month in Utah despite players being largely unable to train under game conditions since March.
Specifically with regard to Rapinoe, Predmore said last week that the two had been in communication as details of the tournament were worked out.
"If she chooses not to play, that's her right to do so," he said.
Rapinoe, 34, is the reigning Ballon d'Or winner and won the Golden Ball as the best player in the 2019 FIFA Women's World Cup.
She will co-host a virtual edition of The ESPYS on June 21 along with Seattle Storm guard Sue Bird and Seattle Seahawks quarterback Russell Wilson.